Question

Rewrite each expression by completing the square q^2+12q+32

Answer 1

The given expression can be written as $q^{2} +12q+32$ = (q+8)(q+4).

Step-by-step explanation:

Given,

$q^{2} +12q+32$

To make it a complete square.

Formula

(a+b)² = $a^{2} +2ab+b^{2}$

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

Now,

$q^{2} +12q+32$

= $q^{2} +2.q.6+6^{2} -6^{2} +32$

= (q+6)²-36+32

= (q+6)²-4

= (q+6)²-2²

= (q+6+2)(q+6-2)

= (q+8)(q+4)