Question

Simplify, giving the answers in factors :

(a + 1) (a - 18) + (a - 2) (a + 15) 

(a) 2(a - 6) (a - 4)

(b) 2(a - 6) (a + 4)

(c) 2(a - 4) (a + 6)

(d) 2(a + 6) (a + 4)

Answer 1

Correct option is (b) 2(a - 6) (a + 4)

(a + 1)(a − 18) + (a − 2)(a + 15)

⇒ (a² + a − 18a − 18) + (a² − 2a + 15a − 30)

⇒ a² − 17a − 18 + a² + 13a − 30

⇒ 2a² − 4a − 48

⇒ 2(a² − 2ab− 24)

⇒ 2(a² − 6a + 4a − 24)

⇒ 2(a(a − 6) + 4(a − 6))

⇒ 2(a − 6)(a + 4)