Question

Factorize the following algebraic expression:

$a^2+2ab+b^2-16$

Answer 1

Given: $a^2+2ab+b^2-16$

Using the formula, $(x+y{)}^2=x^2+2xy+y^2$

$\therefore (a^2+2ab+b^2)-16$

$=(a+b{)}^2-16$

$=(a+b{)}^2-4^2$

Using, $(x^2-y^2)=(x+y)(x-y)$

$=(a+b+4)(a+b-4)$

$\therefore a^2+2ab+b^2-16=(a+b+4)(a+b-4)$