Question

Factorize each of the following algebraic expression:
(a + 7)(a − 10) + 16

Answer 1

$$\begin{gathered} (a+7)(a-10)+16 \\ =a^2-10a+7a-70+16 \\ =a^2-3a-54 \\ Tofactorise{a}^2-3a-54,wewillfindtwonumberspandqsuchthatp+q=-3andpq=-54. \\ Now, \\ 6+(-9)=-3 \\ and \\ 6\times (-9)=-54 \\ Splittingthemiddleterm-3ainthegivenquadraticas-9a+6a,weget: \\ {a}^2-3a-54=a^2-9a+6a-54 \\ =(a^2-9a)+(6a-54) \\ =a(a-9)+6(a-9) \\ =(a+6)(a-9) \end{gathered}$$