Question

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

Answer 1

(q+6)^2 - 4

Explanation:

Answer 2

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

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)