Complete the following table. Algebraic expressions Factorisation by common factors 2 x + 4 2 × x + 2 × 2 = 2 x + 2 5 x y + 10 x

The given algebraic expression can be factorised as, 5 x y + 10 x = 5 × x × y + 10 × x = 5 × x × y + 2 × 5 × x = 5 x y + 2 Hence, the table can be completed as, Algebraic expressions Factorisation by common factors 2 x + 4 2 × x + 2 × 2 = 2 x + 2 5 x y + 10 x 5 × x × y + 2 × 5 × x = 5 x ( y + 2 )

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 )