# ALGEBRA RULES : EXPLANATION OF RULES FOR REMOVAL AND INSERTING OF BRACKETS WITH EXAMPLES

Algebra Simplify before Algebra Rules
if you have not already done so.

### Algebra Rules for Removal of Brackets

If there is a plus, '+' sign before the brackets, then the signs of terms withinbrackets remain unchanged after removing the brackets.

If there is a minus, '-' sign before the brackets, then the signs of terms withinbrackets change, after removing the brackets.

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### Rules for Inserting of Brackets : Algebra Rules

These rules are similar to the above.

If plus, '+' sign is to be there
before the brackets to be inserted,
then the terms within the brackets
need be written without any change
in their signs.

If minus, '-' sign is to be there
before the brackets to be inserted,
then the terms within the brackets
need be written after changing
their signs.

Let us see two Examples
one on Removal and
one on Insertion of brackets.

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### Example 1 of Algebra Rules

Simplify 5x - [7y - {2x - (5y - 2x) - 8y} - 6x]

Solution:
5x - [7y - {2x - (5y - 2x) - 8y} - 6x]
= 5x - [7y - {2x - 5y + 2x - 8y} - 6x] [ Removing ( ) ]
= 5x - [7y - {4x - 13y} - 6x]
= 5x - [7y - 4x + 13y - 6x] [ Removing { } ]
= 5x - [20y - 10x]
= 5x - 20y + 10x [ Removing [ ] ]
= 15x - 20y

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### Example 2 of Algebra Rules

Write the first two terms and last two terms of the expression
-2x + 3y + 4z + 5l - 6m within brackets keeping
(i) plus, '+' sign and (ii) minus '-' sign before the brackets.

Solution to Example 2 of Algebra Rules:
(i) -2x + 3y + 4z + 5l - 6m = +(-2x + 3y) + 4z +(5l - 6m) Ans.
(ii) -2x + 3y + 4z + 5l - 6m = -(2x - 3y) + 4z -(-5l + 6m) Ans.

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