The use of square brackets in Russian. The rule for opening brackets when working

Parentheses are used to indicate the order in which actions are performed in numeric and alphabetic expressions, as well as in expressions with variables. It is convenient to pass from an expression with brackets to identically equal expression without brackets. This technique is called parenthesis opening.

To expand brackets means to rid the expression of these brackets.

Another point deserves special attention, which concerns the peculiarities of writing solutions when opening brackets. We can write down initial expression with brackets and the result obtained after opening the brackets as an equality. For example, after opening the parentheses, instead of the expression
3−(5−7) we get the expression 3−5+7. We can write both of these expressions as the equality 3−(5−7)=3−5+7.

And one more important point. In mathematics, to reduce entries, it is customary not to write a plus sign if it is the first in an expression or in brackets. For example, if we add two positive numbers, for example, seven and three, then we write not +7 + 3, but simply 7 + 3, despite the fact that seven is also a positive number. Similarly, if you see, for example, the expression (5 + x) - know that there is a plus in front of the bracket, which is not written, and there is a plus + (+5 + x) in front of the five.

Bracket expansion rule for addition

When opening brackets, if there is a plus before the brackets, then this plus is omitted along with the brackets.

Example. Open the brackets in the expression 2 + (7 + 3) Before the brackets plus, then the characters in front of the numbers in the brackets do not change.

2 + (7 + 3) = 2 + 7 + 3

The rule for expanding brackets when subtracting

If there is a minus before the brackets, then this minus is omitted along with the brackets, but the terms that were in the brackets change their sign to the opposite. The absence of a sign before the first term in parentheses implies a + sign.

Example. Open brackets in expression 2 − (7 + 3)

There is a minus before the brackets, so you need to change the signs before the numbers from the brackets. There is no sign in brackets before the number 7, which means that the seven is positive, it is considered that the + sign is in front of it.

2 − (7 + 3) = 2 − (+ 7 + 3)

When opening the brackets, we remove the minus from the example, which was before the brackets, and the brackets themselves 2 − (+ 7 + 3), and change the signs that were in the brackets to the opposite ones.

2 − (+ 7 + 3) = 2 − 7 − 3

Expanding parentheses when multiplying

If there is a multiplication sign in front of the brackets, then each number inside the brackets is multiplied by the factor in front of the brackets. At the same time, multiplying a minus by a minus gives a plus, and multiplying a minus by a plus, like multiplying a plus by a minus, gives a minus.

Thus, parentheses in products are expanded in accordance with the distributive property of multiplication.

Example. 2 (9 - 7) = 2 9 - 2 7

When multiplying parenthesis by parenthesis, each term of the first parenthesis is multiplied with every term of the second parenthesis.

(2 + 3) (4 + 5) = 2 4 + 2 5 + 3 4 + 3 5

In fact, there is no need to remember all the rules, it is enough to remember only one, this one: c(a−b)=ca−cb. Why? Because if we substitute one instead of c, we get the rule (a−b)=a−b. And if we substitute minus one, we get the rule −(a−b)=−a+b. Well, if you substitute another bracket instead of c, you can get the last rule.

Expand parentheses when dividing

If there is a division sign after the brackets, then each number inside the brackets is divisible by the divisor after the brackets, and vice versa.

Example. (9 + 6) : 3=9: 3 + 6: 3

How to expand nested parentheses

If the expression contains nested brackets, then they are expanded in order, starting with external or internal.

At the same time, when opening one of the brackets, it is important not to touch the other brackets, just rewriting them as they are.

Example. 12 - (a + (6 - b) - 3) = 12 - a - (6 - b) + 3 = 12 - a - 6 + b + 3 = 9 - a + b

Bracket expansion is a type of expression transformation. In this section, we will describe the rules for expanding brackets, as well as consider the most common examples of tasks.

Yandex.RTB R-A-339285-1

What is parenthesis expansion?

Parentheses are used to indicate the order in which actions are performed in numeric and alphabetic expressions, as well as in expressions with variables. It is convenient to pass from an expression with brackets to an identically equal expression without brackets. For example, replace the expression 2 (3 + 4) with an expression like 2 3 + 2 4 without brackets. This technique is called parenthesis opening.

Definition 1

Under the opening of brackets, we mean the methods of getting rid of brackets and are usually considered in relation to expressions that may contain:

signs "+" or "-" in front of brackets that contain sums or differences;
the product of a number, letter, or several letters, and the sum or difference, which is placed in brackets.

This is how we used to consider the process of expanding brackets in the course school curriculum. However, no one prevents us from looking at this action more broadly. We can call parenthesis expansion the transition from an expression that contains negative numbers in parentheses to an expression that does not have parentheses. For example, we can go from 5 + (− 3) − (− 7) to 5 − 3 + 7 . In fact, this is also parenthesis expansion.

In the same way, we can replace the product of expressions in brackets of the form (a + b) · (c + d) with the sum a · c + a · d + b · c + b · d . This technique also does not contradict the meaning of parentheses expansion.

Here is another example. We can assume that in expressions, instead of numbers and variables, any expressions can be used. For example, the expression x 2 1 a - x + sin (b) will correspond to an expression without brackets of the form x 2 1 a - x 2 x + x 2 sin (b) .

One more point deserves special attention, which concerns the peculiarities of writing solutions when opening brackets. We can write the initial expression with brackets and the result obtained after opening the brackets as equality. For example, after opening the parentheses, instead of the expression 3 − (5 − 7) we get the expression 3 − 5 + 7 . We can write both of these expressions as the equality 3 − (5 − 7) = 3 − 5 + 7 .

Performing actions with cumbersome expressions may require writing intermediate results. Then the solution will have the form of a chain of equalities. For example, 5 − (3 − (2 − 1)) = 5 − (3 − 2 + 1) = 5 − 3 + 2 − 1 or 5 − (3 − (2 − 1)) = 5 − 3 + (2 − 1) = 5 − 3 + 2 − 1 .

Rules for opening brackets, examples

Let's start with the rules for opening parentheses.

Single numbers in brackets

Negative numbers in parentheses often appear in expressions. For example, (− 4) and 3 + (− 4) . Positive numbers in brackets also take place.

Let us formulate the rule for opening brackets that contain single positive numbers. Suppose a is any positive number. Then we can replace (a) with a, + (a) with + a, - (a) with - a. If instead of a we take specific number, then according to the rule: the number (5) will be written as 5 , the expression 3 + (5) without brackets will take the form 3 + 5 , since + (5) is replaced by + 5 , and the expression 3 + (− 5) is equivalent to the expression 3 − 5 , as + (− 5) is replaced by − 5 .

Positive numbers are usually written without using parentheses, since the parentheses are redundant in this case.

Now consider the rule for opening brackets that contain a single a negative number. + (−a) we replace with − a, − (− a) is replaced by + a . If the expression starts with a negative number (-a), which is written in brackets, then the brackets are omitted and instead of (-a) remains − a.

Here are some examples: (− 5) can be written as − 5 , (− 3) + 0 , 5 becomes − 3 + 0 , 5 , 4 + (− 3) becomes 4 − 3 , and − (− 4) − (− 3) after opening the brackets takes the form 4 + 3 , since − (− 4) and − (− 3) is replaced by + 4 and + 3 .

It should be understood that the expression 3 · (− 5) cannot be written as 3 · − 5. About it we will talk in the following paragraphs.

Let's see what the parenthesis expansion rules are based on.

According to the rule, the difference a − b is equal to a + (− b) . Based on the properties of actions with numbers, we can make a chain of equalities (a + (− b)) + b = a + ((− b) + b) = a + 0 = a which will be fair. This chain of equalities, by virtue of the meaning of subtraction, proves that the expression a + (− b) is the difference a-b.

Based on properties opposite numbers and the rules for subtracting negative numbers, we can state that − (− a) = a , a − (− b) = a + b .

There are expressions that are made up of a number, minus signs and several pairs of brackets. Using the above rules allows you to sequentially get rid of brackets, moving from inner brackets to outer or into reverse direction. An example of such an expression would be − (− ((− (5)))) . Let's open the brackets, moving from the inside to the outside: − (− ((− (5)))) = − (− ((− 5))) = − (− (− 5)) = − (5) = − 5 . This example can also be parsed in reverse: − (− ((− (5)))) = ((− (5))) = (− (5)) = − (5) = − 5 .

Under a and b can be understood not only as numbers, but also as arbitrary numerical or literal expressions with a "+" in front that are not sums or differences. In all these cases, you can apply the rules in the same way as we did with single numbers in brackets.

For example, after opening the brackets, the expression − (− 2 x) − (x 2) + (− 1 x) − (2 x y 2: z) takes the form 2 x − x 2 − 1 x − 2 x y 2: z . How did we do it? We know that − (− 2 x) is + 2 x , and since this expression comes first, then + 2 x can be written as 2 x , - (x 2) = - x 2, + (− 1 x) = − 1 x and − (2 x y 2: z) = − 2 x y 2: z.

In the products of two numbers

Let's start with the rule for expanding brackets in the product of two numbers.

Let's pretend that a and b are two positive numbers. In this case, the product of two negative numbers − a and − b of the form (− a) (− b) can be replaced by (a b) , and the products of two numbers with opposite signs of the form (− a) b and a (− b) are replaced by (− a b). Multiplying a minus by a minus gives a plus, and multiplying a minus by a plus, like multiplying a plus by a minus, gives a minus.

The correctness of the first part of the written rule is confirmed by the rule for multiplying negative numbers. To confirm the second part of the rule, we can use the rules for multiplying numbers with different signs.

Let's look at a few examples.

Example 1

Consider the algorithm for opening brackets in the product of two negative numbers - 4 3 5 and - 2 , of the form (- 2) · - 4 3 5 . To do this, we replace the original expression with 2 · 4 3 5 . Let's expand the brackets and get 2 · 4 3 5 .

And if we take the quotient of negative numbers (− 4) : (− 2) , then the record after opening the brackets will look like 4: 2

Instead of negative numbers − a and − b can be any expressions with a leading minus sign that are not sums or differences. For example, these can be products, partials, fractions, degrees, roots, logarithms, trigonometric functions etc.

Let's open the brackets in the expression - 3 · x x 2 + 1 · x · (- ln 5) . According to the rule, we can make the following transformations: - 3 x x 2 + 1 x (- ln 5) = - 3 x x 2 + 1 x ln 5 = 3 x x 2 + 1 x ln 5 .

Expression (− 3) 2 can be converted to the expression (− 3 2) . After that, you can open the brackets: − 3 2.

2 3 - 4 5 = - 2 3 4 5 = - 2 3 4 5

Dividing numbers with different signs may also require the preliminary expansion of brackets: (− 5) : 2 = (− 5: 2) = − 5: 2 and 2 3 4: (- 3 , 5) = - 2 3 4: 3 , 5 = - 2 3 4: 3 , 5 .

The rule can be used to perform multiplication and division of expressions with different signs. Let's give two examples.

1 x + 1: x - 3 = - 1 x + 1: x - 3 = - 1 x + 1: x - 3

sin (x) (- x 2) \u003d (- sin (x) x 2) \u003d - sin (x) x 2

In the products of three or more numbers

Let's move on to the product and the quotients, which contain large quantity numbers. For expanding brackets, the following rule will apply here. With an even number of negative numbers, you can omit the parentheses, replacing the numbers with their opposites. After that, you need to enclose the resulting expression in new brackets. For an odd number of negative numbers, omitting the brackets, replace the numbers with their opposites. After that, the resulting expression must be taken in new brackets and put a minus sign in front of it.

Example 2

For example, let's take the expression 5 · (− 3) · (− 2) , which is the product of three numbers. There are two negative numbers, so we can write the expression as (5 3 2) and then finally open the brackets, getting the expression 5 3 2 .

In the product (− 2 , 5) (− 3) : (− 2) 4: (− 1 , 25) : (− 1) five numbers are negative. so (− 2 , 5) (− 3) : (− 2) 4: (− 1 , 25) : (− 1) = (− 2 . 5 3: 2 4: 1 , 25: 1) . Finally opening the brackets, we get −2.5 3:2 4:1.25:1.

The above rule can be justified as follows. First, we can rewrite such expressions as a product, replacing division with multiplication by the reciprocal. We represent each negative number as the product of a multiplier and replace - 1 or - 1 with (− 1) a.

Using the commutative property of multiplication, we swap the factors and transfer all factors equal to − 1 , to the beginning of the expression. The product of an even number minus ones is equal to 1, and an odd number is equal to − 1 , which allows us to use the minus sign.

If we did not use the rule, then the chain of actions for opening brackets in the expression - 2 3: (- 2) 4: - 6 7 would look like this:

2 3: (- 2) 4: - 6 7 = - 2 3 - 1 2 4 - 7 6 = = (- 1) 2 3 (- 1) 1 2 4 (- 1 ) 7 6 = = (- 1) (- 1) (- 1) 2 3 1 2 4 7 6 = (- 1) 2 3 1 2 4 7 6 = = - 2 3 1 2 4 7 6

The above rule can be used when expanding brackets in expressions that are products and quotients with a minus sign that are not sums or differences. Take for example the expression

x 2 (- x) : (- 1 x) x - 3: 2 .

It can be reduced to an expression without brackets x 2 · x: 1 x · x - 3: 2 .

Opening parentheses preceded by a + sign

Consider a rule that can be applied to expand brackets that are preceded by a plus sign and the "contents" of those brackets are not multiplied or divided by any number or expression.

According to the rule, brackets together with the sign in front of them are omitted, while the signs of all terms in brackets are preserved. If there is no sign in front of the first term in brackets, then you need to put a plus sign.

Example 3

For example, we give the expression (12 − 3 , 5) − 7 . By omitting the brackets, we keep the signs of the terms in the brackets and put a plus sign in front of the first term. The entry will look like (12 − 3 , 5) − 7 = + 12 − 3 , 5 − 7 . In the above example, it is not necessary to put a sign in front of the first term, since + 12 - 3, 5 - 7 = 12 - 3, 5 - 7.

Example 4

Let's consider one more example. Take the expression x + 2 a - 3 x 2 + 1 - x 2 - 4 + 1 x and perform actions with it x + 2 a - 3 x 2 + 1 - x 2 - 4 + 1 x = = x + 2 a - 3 x 2 + 1 - x 2 - 4 + 1 x

Here is another example of expanding parentheses:

Example 5

2 + x 2 + 1 x - x y z + 2 x - 1 + (- 1 + x - x 2) = = 2 + x 2 + 1 x - x y z + 2 x - 1 - 1 + x + x2

How to expand parentheses preceded by a minus sign

Consider cases where there is a minus sign in front of the brackets, and which are not multiplied (or divided) by any number or expression. According to the rule for opening brackets preceded by the “-” sign, the brackets with the “-” sign are omitted, while the signs of all terms inside the brackets are reversed.

Example 6

For example:

1 2 \u003d 1 2, - 1 x + 1 \u003d - 1 x + 1, - (- x 2) \u003d x 2

Variable expressions can be converted using the same rule:

X + x 3 - 3 - - 2 x 2 + 3 x 3 x + 1 x - 1 - x + 2,

we get x - x 3 - 3 + 2 x 2 - 3 x 3 x + 1 x - 1 - x + 2 .

Opening parentheses when multiplying a number by a parenthesis, expressions by a parenthesis

Here we will consider cases when it is necessary to open brackets that are multiplied or divided by any number or expression. Here formulas of the form (a 1 ± a 2 ± ... ± a n) b = (a 1 b ± a 2 b ± ... ± a n b) or b (a 1 ± a 2 ± … ± a n) = (b a 1 ± b a 2 ± … ± b a n), where a 1 , a 2 , … , a n and b are some numbers or expressions.

Example 7

For example, let's expand the brackets in the expression (3 − 7) 2. According to the rule, we can make the following transformations: (3 − 7) 2 = (3 2 − 7 2) . We get 3 · 2 − 7 · 2 .

Expanding the brackets in the expression 3 x 2 1 - x + 1 x + 2, we get 3 x 2 1 - 3 x 2 x + 3 x 2 1 x + 2.

Multiply a parenthesis by a parenthesis

Consider the product of two brackets of the form (a 1 + a 2) · (b 1 + b 2) . This will help us get a rule for expanding parentheses when multiplying a parenthesis by a parenthesis.

In order to solve the above example, we denote the expression (b 1 + b 2) like b. This will allow us to use the parenthesis-expression multiplication rule. We get (a 1 + a 2) (b 1 + b 2) = (a 1 + a 2) b = (a 1 b + a 2 b) = a 1 b + a 2 b . By doing a reverse substitution b on (b 1 + b 2), again apply the rule for multiplying the expression by the bracket: a 1 b + a 2 b = = a 1 (b 1 + b 2) + a 2 (b 1 + b 2) = = (a 1 b 1 + a 1 b 2) + (a 2 b 1 + a 2 b 2) = = a 1 b 1 + a 1 b 2 + a 2 b 1 + a 2 b 2

Thanks to a number of simple tricks, we can come to the sum of the products of each of the terms from the first bracket and each of the terms from the second bracket. The rule can be extended to any number of terms inside the brackets.

Let us formulate the rules for multiplying brackets by brackets: in order to multiply two sums among themselves, it is necessary to multiply each of the terms of the first sum by each of the terms of the second sum and add the results.

The formula will look like:

(a 1 + a 2 + . . . + a m) (b 1 + b 2 + . . . + b n) = = a 1 b 1 + a 1 b 2 + . . . + a 1 b n + + a 2 b 1 + a 2 b 2 + . . . + a 2 b n + + . . . + + a m b 1 + a m b 1 + . . . a m b n

Let's expand the brackets in the expression (1 + x) · (x 2 + x + 6) It is a product of two sums. Let's write the solution: (1 + x) (x 2 + x + 6) = = (1 x 2 + 1 x + 1 6 + x x 2 + x x + x 6) = = 1 x 2 + 1 x + 1 6 + x x 2 + x x + x 6

Separately, it is worth dwelling on those cases when there is a minus sign in brackets along with plus signs. For example, let's take the expression (1 − x) · (3 · x · y − 2 · x · y 3) .

First, we represent the expressions in brackets as sums: (1 + (− x)) (3 x y + (− 2 x y 3)). Now we can apply the rule: (1 + (− x)) (3 x y + (− 2 x y 3)) = = (1 3 x y + 1 (− 2 x y 3) + (− x) 3 x y + (− x) (− 2 x y 3))

Let's expand the brackets: 1 3 x y − 1 2 x y 3 − x 3 x y + x 2 x y 3 .

Parentheses expansion in products of several brackets and expressions

If there are three or more expressions in brackets in the expression, it is necessary to expand the brackets sequentially. It is necessary to start the transformation with the fact that the first two factors are taken in brackets. Inside these brackets, we can perform transformations according to the rules discussed above. For example, the parentheses in the expression (2 + 4) 3 (5 + 7 8) .

The expression contains three factors at once (2 + 4) , 3 and (5 + 7 8) . We will expand the brackets sequentially. We enclose the first two factors in one more brackets, which we will make red for clarity: (2 + 4) 3 (5 + 7 8) = ((2 + 4) 3) (5 + 7 8).

In accordance with the rule of multiplying a bracket by a number, we can carry out the following actions: ((2 + 4) 3) (5 + 7 8) = (2 3 + 4 3) (5 + 7 8) .

Multiply bracket by bracket: (2 3 + 4 3) (5 + 7 8) = 2 3 5 + 2 3 7 8 + 4 3 5 + 4 3 7 8 .

Parenthesis in kind

Powers whose bases are some expressions written in brackets, with natural indicators can be thought of as a product of several parentheses. Moreover, according to the rules from the two previous paragraphs, they can be written without these brackets.

Consider the process of transforming the expression (a + b + c) 2 . It can be written as a product of two brackets (a + b + c) (a + b + c). We multiply bracket by bracket and get a a + a b + a c + b a + b b + b c + c a + c b + c c .

Let's take another example:

Example 8

1 x + 2 3 = 1 x + 2 1 x + 2 1 x + 2 = = 1 x 1 x + 1 x 2 + 2 1 x + 2 2 1 x + 2 = = 1 x 1 x 1 x + 1 x 2 1 x + 2 1 x 1 x + 2 2 1 x + 1 x 1 x 2 + + 1 x 2 2 + 2 1 x 2 + 2 2 2

Dividing a parenthesis by a number and a parenthesis by a parenthesis

Dividing a parenthesis by a number suggests that you must divide by the number all the terms enclosed in brackets. For example, (x 2 - x) : 4 = x 2: 4 - x: 4 .

Division can be previously replaced by multiplication, after which you can use the appropriate rule for opening brackets in the product. The same rule applies when dividing a parenthesis by a parenthesis.

For example, we need to open the brackets in the expression (x + 2) : 2 3 . To do this, first replace the division by multiplying by the reciprocal of (x + 2) : 2 3 = (x + 2) · 2 3 . Multiply the bracket by the number (x + 2) 2 3 = x 2 3 + 2 2 3 .

Here is another example of parenthesis division:

Example 9

1 x + x + 1: (x + 2) .

Let's replace division with multiplication: 1 x + x + 1 1 x + 2 .

Let's do the multiplication: 1 x + x + 1 1 x + 2 = 1 x 1 x + 2 + x 1 x + 2 + 1 1 x + 2 .

Bracket expansion order

Now consider the order of application of the rules discussed above in the expressions general view, i.e. in expressions that contain sums with differences, products with quotients, brackets in kind.

The order of actions:

the first step is to raise the parentheses to a natural power;
at the second stage, brackets are opened in works and private;
the final step is to open the brackets in the sums and differences.

Let's consider the order of actions using the example of the expression (− 5) + 3 · (− 2) : (− 4) − 6 · (− 7) . Let us transform from the expressions 3 (− 2) : (− 4) and 6 (− 7) , which should take the form (3 2:4) and (− 6 7) . Substituting the obtained results into the original expression, we obtain: (− 5) + 3 (− 2) : (− 4) − 6 (− 7) = (− 5) + (3 2: 4) − (− 6 7). Expand the brackets: − 5 + 3 2: 4 + 6 7 .

When dealing with expressions that contain parentheses within parentheses, it is convenient to perform transformations from the inside out.

If you notice a mistake in the text, please highlight it and press Ctrl+Enter

Everywhere. Everywhere and everywhere, wherever you look, there are such constructions:

These "constructions" in literate people cause an ambiguous reaction. At least like "is it really so - right?".
In general, personally, I can’t understand where the “fashion” of not closing external quotes came from. The first and only analogy that comes up in this regard is the analogy with brackets. Nobody doubts that two brackets in a row are normal. For example: "Pay for the entire circulation (200 pieces (of which 100 are defective))". But in the normality of setting two quotes in a row, someone doubted (I wonder who is the first?) ... And now everyone without exception has become clear conscience to produce constructions of the type LLC "Firma" Pupkov and Co. ".
But even if you have not seen the rule in your life, which will be discussed below, then the only logically justified option (using the brackets as an example) would be the following: Firm Pupkov and Co LLC.
So, the rule itself:
If at the beginning or at the end of a quotation (the same applies to direct speech) there are internal and external quotation marks, then they must differ from each other in a pattern (the so-called "herringbones" and "cutes"), and external quotation marks should not be omitted, for example: C The sides of the ship were radioed: "Leningrad has entered the tropics and is continuing on its course." About Zhukovsky, Belinsky writes: “Contemporaries of Zhukovsky’s youth looked at him mainly as an author of ballads, and in one of his messages Batyushkov called him a “ballade player.”
© Rules of Russian spelling and punctuation. - Tula: Autograph, 1995. - 192 p.
Accordingly ... if you do not have the opportunity to type in quotes, "Christmas trees", then what can you do, you will have to use such "" icons. However, the impossibility (or unwillingness) to use Russian quotes is by no means the reason why you can not close the outer quotes.
Thus, it seems that they figured out the incorrect design of Firm Pupkov and Co LLC. There are also constructions of the type LLC Firm Pupkov and Co.
From the rule, it is quite clear that such constructions are illiterate ... (Correct: LLC Firm Pupkov and Co.
However!
Milchin's Publisher's and Author's Handbook (2004 edition) states that two design options can be used in such cases. The use of "herringbones" and "paws" and (in the absence of technical means) the use of only "herringbones": two opening and one closing.
The directory is “fresh” and personally I immediately have 2 questions here. Firstly, with what joy you can still use one closing quote-herringbone (well, this is illogical, see above), and secondly, the phrase “in the absence of technical means” especially attracts attention. How is that, sorry? Here, open Notepad and type “only Christmas trees: two opening and one closing” there. There are no such characters on the keyboard. Printing a Christmas tree doesn't work... The combination Shift + 2 produces the sign " (which, as you know, is not even a quotation mark). Now open Microsoft Word and press Shift + 2 again. The program will correct " to " (or " ). Well, it turns out that the rule that existed for more than a dozen years was taken and rewritten under Microsoft Word? Like, since the Word from "Firm" Pupkov and Co "does" Firm "Pupkov and Co", then now let it be acceptable and correct ???
It seems so. And if so, then there is every reason to doubt the correctness of such an innovation.
Yes, and one more clarification ... about the very "lack of technical means." The fact is that on any computer with Windows there are always " technical means” to enter both “herringbones” and “paws”, so this new “rule” (for me it is in quotes) is incorrect initially!
All special characters in a font can be easily typed by knowing the corresponding number of that character. It is enough to hold down Alt and type on the NumLock keyboard (NumLock is pressed, the indicator light is on) the corresponding symbol number:
„ Alt + 0132 (left foot)
“ Alt + 0147 (right foot)
« Alt + 0171 (left herringbone)
» Alt + 0187 (right herringbone)

If you want to include information related to body text, but that information doesn't fit into the body of a sentence or paragraph, you need to put that information in parentheses. Putting it in parentheses reduces its importance so that it doesn't detract from the main point of the text.

Example: J. R. R. Tolkien (author of The Lord of the Rings) and C. S. Lewis (author of The Chronicles of Narnia) were regular members of the literary discussion group known as the Inklings.

Notes in brackets. Often, when you write a numerical value in words, it is helpful to also write that value in numbers. You can specify a numerical form by putting it in parentheses.

Example: She has to pay seven hundred dollars ($700) in rent by the end of this week.

Use of numbers or letters when listing. When you need to list a series of information within a paragraph or sentence, numbering each paragraph can make the list less confusing. You must put the numbers or letters used for each item in parentheses.

Example: A company is looking for a job candidate who (1) is disciplined, (2) knows everything there is to know about the latest trends in photo editing and enhancements software and (3) has at least five years of professional experience in the field.
Example: A company is looking for a job candidate who (A) is disciplined, (B) knows everything there is to know about the latest trends in photo editing and software improvements, and (C) has at least five years of professional experience in the field.

Plural designation. In text, you can refer to something in the singular while also referring to the plural. If it is known that the reader will benefit from knowing that you mean both the plural and singular, you can indicate your intention by putting in parentheses immediately after the noun the appropriate ending given noun in plural if the noun has this form.

Example: This year's festival organizers hope for a large number of spectators, so be sure to purchase additional ticket(s).

Abbreviations notation. When writing the name of an organization, product, or other entity that usually has well-known abbreviations, you need to include full name object the first time you mention it in the text. If you are going to refer to an object later using a well-known abbreviation, you must specify that abbreviation in parentheses so that readers know what to look for later.

Example: Animal Welfare League (PLL) staff and volunteers hope to reduce and eventually eliminate animal cruelty and mistreatment within the community.

Mention of significant dates. Although not always necessary, in certain contexts you may be required to provide the date of birth and/or date of death of the specific person you are referring to in the text. Such dates must be enclosed in brackets.

Example: Jane Austen (1775-1817) is known for her literary works"Pride and Prejudice" and "Sense and Sensibility"
George Martin (b. 1948) is the man behind the hit series Game of Thrones.

Use of introductory quotes. AT scientific literature, introductory citations should be included in the text when you directly or indirectly cite another work. These citations contain bibliographic information and should be enclosed in brackets immediately after the borrowed information.

Example: Research shows that there is a link between migraine and clinical depression (Smith, 2012).
Example: Research shows that there is a link between migraine and clinical depression (Smith 32).
To receive additional information about correct use in the text of introductory quotations, see "How to correctly use quotations in the text."