Question

factor completely. 162t^{2}+288t + 128

Explanation:

Step1: Factor out the greatest - common factor

First, find the GCF of 162, 288, and 128. The GCF of 162, 288, and 128 is 2.
$162t^{2}+288t + 128=2(81t^{2}+144t + 64)$

Step2: Recognize the perfect - square trinomial

The trinomial $81t^{2}+144t + 64$ is in the form $a^{2}+2ab + b^{2}$, where $a = 9t$ and $b = 8$ since $(9t)^{2}=81t^{2}$, $2\times9t\times8 = 144t$, and $8^{2}=64$.
$81t^{2}+144t + 64=(9t + 8)^{2}$

Answer:

$2(9t + 8)^{2}$