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

Please study
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 within brackets remain unchanged after removing the brackets.

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

Rules for Inserting of Brackets

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.

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

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:
(i) -2x + 3y + 4z + 5l - 6m = +(-2x + 3y) + 4z +(5l - 6m) Ans.
(ii) -2x + 3y + 4z + 5l - 6m = -(2x - 3y) + 4z -(-5l + 6m) Ans.

If you want to learn about
introduction of equations
and the associated terminology
different types of Equations
and their solutions
and the word Problems on Equations,
Go to

Simplifying Equations