Complete the following table. Algebraic expressions Factorisation by common factors 2 x + 4 2 × x + 2 × 2 = 2 x + 2 12 a 2 b + 15 a b 2

The given algebraic expression can be factorised as, 12 a 2 b + 15 a b 2 = 2 × 2 × 3 × a × a × b + 3 × 5 × a × b × b = 3 a b 4 a + 5 b Algebraic expressions Factorisation by common factors 2 x + 4 2 × x + 2 × 2 = 2 x + 2 12 a 2 b + 15 a b 2 3 × 4 × a × a × b + 3 × 5 × a × b × b = 3 a b ( 4 a + 5 b )

Complete the following table. S.No. Algebraic expressions Factorisation by common factors (iv) 10 x 2 - 18 x 3 + 14 x 4

Given algebraic expression is 10 x 2 - 18 x 3 + 14 x 4 ⇒ 10 x 2 - 18 x 3 + 14 x 4 = 2 × 5 × x × x - 2 × 3 × 3 × x × x × x + 2 × 7 × x × x × x × x ⇒ 2 x 2 5 - 9 x + 7 x 2 Hence, the complete table is S.No. Algebraic expressions Factorisation by common factors (iv) 10 x 2 - 18 x 3 + 14 x 4 2 × 5 × x × x - 2 × 3 × 3 × x × x × x + 2 × 7 × x × x × x × x = 2 x 2 ( 5 - 9 x + 7 x 2 )

Complete the following table. S.No. Algebraic expressions Factorisation by common factors (v) 4 x 2 + 18 x + 20

The given expression is 4 x 2 + 18 x + 20 ⇒ 4 x 2 + 18 x + 20 = 2 × 2 × x × x + 2 × 3 × 3 × x + 2 × 2 × 5 = 2 ( 2 x 2 + 9 x + 10 ) Hence, the complete table is S.No. Algebraic expressions Factorisation by common factors (v) 4 x 2 + 18 x + 20 2 × 2 × x × x + 2 × 3 × 3 × x + 2 × 2 × 5 = 2 ( 2 x 2 + 9 x + 10 )

Factorise and complete the table. S.No. Algebraic expressions Factorisation by regrouping terms (ii) 2 x y + 2 y + 3 x + 3 [ 2 x y + 3 x ] + [ 2 y + 3 ] = =

Given algebraic expression is 2 x y + 2 y + 3 x + 3 We know that, in factorization by regrouping sometimes the terms of the given expression need to be arranged in suitable groups in such a way that all the groups have a common factor. After this arrangement factorization becomes easy. By suitably rearranging the terms, we get, ⇒ 2 x y + 2 y + 3 x + 3 = [ 2 x y + 3 x ] + [ 2 y + 3 ] = x 2 y + 3 + 1 ( 2 y + 3 ) = x + 1 2 y + 3 Hence, the complete table is, S.No. Algebraic expressions Factorisation by regrouping terms (ii) 2 x y + 2 y + 3 x + 3 [ 2 x y + 3 x ] + [ 2 y + 3 ] = x 2 y + 3 + 1 ( 2 y + 3 ) = x + 1 2 y + 3

Factorise and complete the table. S.No. Algebraic expressions Factorisation by regrouping terms (iii) 6 x y - 4 y + 6 - 9 x [ 6 x y - 4 y ] + [ 6 - 9 x ] = =

Given algebraic expression is 6 x y - 4 y + 6 - 9 x We know that, in factorization by regrouping sometimes the terms of the given expression need to be arranged in suitable groups in such a way that all the groups have a common factor. After this arrangement factorization becomes easy. By suitably rearranging the terms, we get, ⇒ 6 x y - 4 y + 6 - 9 x = [ 6 x y - 4 y ] + [ 6 - 9 x ] = 2 y 3 x - 2 - 3 ( 3 x - 2 ) = 3 x - 2 2 y - 3 Hence, the complete table is, S.No. Algebraic expressions Factorisation by regrouping terms (iii) 6 x y - 4 y + 6 - 9 x [ 6 x y - 4 y ] + [ 6 - 9 x ] = 2 y 3 x - 2 - 3 ( 3 x - 2 ) = 3 x - 2 2 y - 3

Factorise and complete the table. Algebraic expressions Factorisation by regrouping terms z - 14 + 14 x y - x y z [ z - x y z ] + [ - 14 + 14 x y ] = =

Given algebraic expression is z - 14 + 14 x y - x y z , We know that, in factorization by regrouping sometimes the terms of the given expression need to be arranged in suitable groups in such a way that all the groups have a common factor. After this arrangement factorization becomes easy. By suitably rearranging the terms, we get, ⇒ z - 14 + 14 x y - x y z = [ z - x y z ] + [ - 14 + 14 x y ] ⇒ z - 14 + 14 x y - x y z = z ( 1 - x y ) - 14 ( 1 - x y ) ⇒ z - 14 + 14 x y - x y z = z - 14 1 - x y Hence, the complete table is, Algebraic expressions Factorisation by regrouping terms z - 14 + 14 x y - x y z [ z - x y z ] + [ - 14 + 14 x y ] = z ( 1 - x y ) - 14 ( 1 - x y ) = z - 14 1 - x y

E M B I B E

NCERT Practice Workbook Mathematics>Chapter 14 - Factorisation>Worksheet 1

Subject Experts Solutions for Chapter: Factorisation, Exercise 1: Worksheet 1

Author:Subject Experts

Subject Experts Mathematics Solutions for Exercise - Subject Experts Solutions for Chapter: Factorisation, Exercise 1: Worksheet 1

Attempt the practice questions on Chapter 14: Factorisation, Exercise 1: Worksheet 1 with hints and solutions to strengthen your understanding. NCERT Practice Workbook Mathematics solutions are prepared by Experienced Embibe Experts.