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How to open brackets?

Ildar Yunusov
Ildar Yunusov
July 25, 2014
36694
How to open brackets?

In this article we will examine in detail the basic rules of such an important topic of the course of mathematics as the opening of brackets. Know the rules for the disclosure of brackets is necessary in order to correctly solve the equations in which they are used.

How to unfold brackets when adding

We open the brackets, in front of which is the sign "+"

This is the simplest case, because if there is an addition sign in front of the brackets, when opening the brackets, the signs inside them do not change. Example:

(9 + 3) + (1 – 6 + 9) = 9 + 3 + 1 – 6 + 9 = 16.

How to open the brackets, which are preceded by the sign "-"

In this case, you need to rewrite all the terms without brackets, but at the same time change all the signs inside them to the opposite. Signs are changed only in terms of those brackets, in front of which was a sign “-“. Example:

(9 + 3) - (1 – 6 + 9) = 9 + 3 - 1 + 6 - 9 = 8.

How to open parentheses when multiplying

Before the parentheses is the number factor

In this case, you need to multiply each item by a factor and open the brackets, without changing signs. If the multiplier has a “-” sign, then when multiplying, the terms of the terms are reversed. Example:

3 * (1 – 6 + 9) = 3 * 1 - 3 * 6 + 3 * 9 = 3 – 18 + 27 = 12.

How to open two brackets with multiplication between them

In this case, you need to multiply each term from the first brackets with each term from the second brackets and then add the results. Example:

(9 + 3) * (1 – 6 + 9) = 9 * 1 + 9 * (- 6) + 9 * 9 + 3 * 1 + 3 * (- 6) + 3 * 9 = 9 – 54 + 81 + 3 – 18 + 27 = 48.

How to open brackets in a square

If the sum or difference of the two terms is squared, the brackets should be opened by the following formula:

(x + y) ^ 2 = x ^ 2 + 2 * x * y + y ^ 2.

In the case of a minus inside the parentheses, the formula does not change. Example:

(9 + 3) ^ 2 = 9 ^ 2 + 2 * 9 * 3 + 3 ^ 2 = 144.

How to open parentheses to a different degree

If the sum or difference of terms is raised, for example, to the 3rd or 4th degree, then you just need to divide the degree of the bracket into “squares”. The degrees of the same factors are added, and when dividing, the divisor degree is subtracted from the degree of the dividend. Example:

(9 + 3) ^ 3 = ((9 + 3) ^ 2) * (9 + 3) = (9 ^ 2 + 2 * 9 * 3 + 3 ^ 2) * 12 = 1728.

How to open 3 brackets

There are equations in which 3 brackets are multiplied at once. In this case, you must first multiply the terms of the first two brackets, and then multiply the sum of this multiplication by the terms of the third bracket. Example:

( 1 + 2 ) * ( 3 + 4 ) * ( 5 - 6 ) = ( 3 + 4 + 6 + 8 ) * ( 5 – 6) = - 21.

These rules for the disclosure of brackets are equally distributed to solve both linear and trigonometric equations.

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