Question

factor the trinomial, if possible.\\(18c^{2} + 24cg + 8g^{2}\\)

Explanation:

Step1: Factor out GCF

Find GCF of 18,24,8: 2
$2(9c^2 + 12cg + 4g^2)$

Step2: Factor quadratic inside

Match $a^2+2ab+b^2=(a+b)^2$, where $a=3c$, $b=2g$
$9c^2 + 12cg + 4g^2=(3c+2g)^2$

Step3: Combine results

Substitute factored quadratic back
$2(3c+2g)^2$

Answer:

$2(3c + 2g)^2$