Question

factor the following trinomial.
$16x^2 + 72x + 81$
$(?x + \box)^2$

Explanation:

Step1: Identify perfect square terms

$16x^2=(4x)^2$, $81=9^2$

Step2: Verify middle term

Check $2\times4x\times9=72x$, matches the trinomial's middle term.

Step3: Write as square of binomial

The trinomial fits $(a+b)^2=a^2+2ab+b^2$ where $a=4x$, $b=9$.

Answer:

$(4x + 9)^2$