Question

Factorize each of the following algebraic expressions :

$(a+7)(a-10)+16$

Answer 1

$(a+7)(a-10)+16(a+7)(a-10)+16=a^2+(7-10)a+7\times (-10)+16\left\{\right(x+a\left)\right(x+b)=x^2+(a+b)x+ab\}=a^2-3a-70+16=a^2-3a-54=a^2-9a+6a-54\left\{\begin{array}{c}-54=-9\times 6\\ -3=-9+6\end{array}\right\}=a(a-9)+6(a-9)=(a-9)(a+6)$