CLASS-8SIMPLIFICATION OF ALGEBRAIC EXPRESSION

SIMPLIFICATION OF ALGEBRAIC EXPRESSION-

The rules for the simplification of an algebraic expression are the same as the rules used for numbers.

Removal of Brackets –

Brackets in an algebraic expression are opened in the order,  ͞   ( Line Bracket), ( ), { }, and [ ]. The rules for opening brackets are as follows.

Rules.1) If there is a + (Positive) sign outside a brackets, the bracket is removed without changing the signs of the terms inside the bracket.

Rules.2) If there is a – (negative) sign outside a bracket, the bracket is removed after changing the signs of all the terms inside the bracket.

Example.1) Simplify 10xy – 5x ( y + 2 ) + 7x² - 2x ( 7x – 8y ) – { 8y ( 2x + y ) + 12 }

Ans.)  10xy – 5x (y + 2) + 7x² - 2x ( 7x – 8y ) – { 8y ( 2x + y ) + 12 }

=  10xy – 5x (y + 2) + 7x² - 2x ( 7x – 8y ) – 16xy – 8y² - 12

=  10xy – 5xy – 10x + 7x² - 14x² + 16xy – 16xy – 8y² - 12

=   5xy – 7x² - 10x – 8y² - 12                  (Ans.)

Example.2) Simplify 8x²y² – 10x (2x + 3y) - 7x²y + { 2x ( 3x – 8y ) + 5xy ( 5x - 2y ) - 12 }

Ans.) 8x²y² – 10x (2x + 3y) - 7x²y + { 2x ( 3x – 8y ) + 5xy ( 5x - 2y ) - 12 }

= 8x²y² – 10x (2x + 3y) - 7x²y + { 6x² - 16xy + 25x²y – 10xy² - 12}

= 8x²y² – 10x (2x + 3y) - 7x²y + 6x² - 16xy + 25x²y – 10xy² - 12

= 8x²y² – 20x² - 30xy – 7x²y + 6x² - 16xy + 25x²y – 10xy² - 12

= 8x²y² - 14x² - 46xy + 18x²y – 10xy² - 12         (Ans.)