Question

Factorize the following algebraic expression:

$49-a^2+8ab-16b^2$

Answer 1

Given: $49-a^2+8ab-16b^2$

$=49-(a^2-8ab+16b^2)$
$=49-\left[\right(a{)}^2-2\left(a\right)\left(4b\right)+\left(4b{)}^2\right]$
Using, $(x-y{)}^2=x^2-2xy+y^2$
$=49-(a-4b{)}^2$
$=7^2-(a-4b{)}^2$
Using, $x^2-y^2=(x+y)(x-y)$
$=[7+(a-4b\left)\right][7-(a-4b\left)\right]$
$=(a-4b+7)(-a+4b+7)$
$=-(a-4b+7)(a-4b-7)$

$\therefore 49-a^2+8ab-16b^2=-(a-4b+7)(a-4b-7)$