Divide. 5 p q ( p 2 - q 2 ) ÷ 2 p ( p + q ) .

We have to divide 5 p q ( p 2 - q 2 ) by 2 p ( p + q ) . 5 p q ( p 2 - q 2 ) ÷ 2 p ( p + q ) = 5 p q ( p 2 - q 2 ) 2 p ( p + q ) = 5 p q ( p + q ) ( p - q ) 2 p ( p + q ) { ( a 2 - b 2 ) = ( a + b ) ( a - b ) } = 5 2 q ( p - q ) Hence, 5 p q ( p 2 - q 2 ) ÷ 2 p ( p + q ) = 5 2 q ( p - q ) .

Divide. ( m 2 - 14 m - 32 ) ÷ ( m + 2 )

( m 2 - 14 m - 32 ) ÷ ( m + 2 ) = m 2 - 14 m - 32 m + 2 = m 2 - 16 m + 2 m - 32 m + 2 = m ( m - 16 ) + 2 ( m - 16 ) m + 2 = ( m - 16 ) ( m + 2 ) m + 2 = ( m - 16 ) Hence, ( m 2 - 14 m - 32 ) ÷ ( m + 2 ) = ( m - 16 ) .

Divide. ( 5 p 2 - 25 p + 20 ) ÷ ( p - 1 )

Given: ( 5 p 2 - 25 p + 20 ) ÷ ( p - 1 ) ( 5 p 2 - 25 p + 20 ) ÷ ( p - 1 ) = ( 5 p 2 - 25 p + 20 ) p - 1 = p 2 - 5 p + 4 p - 1 (Dividing the numerator by 5 ) = p 2 - 4 p - p + 4 p - 1 = p ( p - 4 ) - 1 ( p - 4 ) p - 1 = ( p - 4 ) ( p - 1 ) ( p - 1 ) = p - 4 Hence, ( 5 p 2 - 25 p + 20 ) ÷ ( p - 1 ) = p - 4 .

Divide x 2 4 - x 2 - 12 by x 2 - 4 .

We need to divide x 2 4 - x 2 - 12 by x 2 - 4 . First, we simplify the dividend and the divisor. x 2 4 - x 2 - 12 = x 2 - 2 x - 48 4 and x 2 - 4 = x - 8 2 . So, ( x 2 - 2 x - 48 4 ) ÷ x - 8 2 = x 2 - 2 x - 48 4 x - 8 2 = x 2 - 2 x - 48 x - 8 × 2 4 = x 2 - 2 x - 48 2 x - 16 = x 2 - 8 x + 6 x - 48 2 ( x - 8 ) = x ( x - 8 ) + 6 ( x - 8 ) 2 ( x - 8 ) = ( x - 8 ) ( x + 6 ) 2 ( x - 8 ) = ( x + 6 ) 2 = x 2 + 3 Hence, ( x 2 4 - x 2 - 12 ) ÷ ( x 2 - 4 ) = x 2 + 3 .

E M B I B E

Maths Hub (ICSE)>Chapter 6 - Algebraic Expressions and Identities>CHECK POINT

S Purkayastha Solutions for Chapter: Algebraic Expressions and Identities, Exercise 8: CHECK POINT

Author:S Purkayastha

S Purkayastha Mathematics Solutions for Exercise - S Purkayastha Solutions for Chapter: Algebraic Expressions and Identities, Exercise 8: CHECK POINT

Attempt the free practice questions on Chapter 6: Algebraic Expressions and Identities, Exercise 8: CHECK POINT with hints and solutions to strengthen your understanding. Maths Hub (ICSE) solutions are prepared by Experienced Embibe Experts.