Question

Factorise : 81 − (a−2)^2

Answer 1

(11 - a)(7 + a)

Explanation:

81 - (a - 2)² ← is a difference of squares and factorises in general as

a² - b² = (a - b)(a + b) , then

81 - (a - 2)²

= 9² - (a - 2)²

= (9 - (a - 2) )(9 + (a - 2) )

= (9 - a + 2)(9 + a - 2)

= (11 - a)(7 + a)