Question

Factorize each of the following expression:
a(a − 2b − c) + 2bc

Answer 1

$$a(a-2b-c)+2bc=a^2-2ab-ac+2bc$$
$$=(a^2-ac)+(2bc-2ab)$$ [Regrouping the terms]
$$=a(a-c)+2b(c-a)$$
$$=a(a-c)-2b(a-c)[\because (c-a)=-(a-c)]$$
$$=(a-2b)(a-c)$$ [Taking (a - c) as the common factor]