Question

factor completely.
$162c^{2}-98$

Explanation:

Step1: Factor out GCF

First, find the greatest common factor (GCF) of 162 and 98. The GCF is 2.
$162c^2 - 98 = 2(81c^2 - 49)$

Step2: Recognize difference of squares

Notice $81c^2 - 49$ is a difference of squares: $a^2 - b^2$ where $a=9c$, $b=7$.
$81c^2 - 49 = (9c)^2 - 7^2$

Step3: Apply difference of squares rule

Use the formula $a^2 - b^2=(a+b)(a-b)$.
$(9c)^2 - 7^2 = (9c+7)(9c-7)$

Step4: Combine factors

Substitute back into the expression from Step1.
$2(81c^2 - 49) = 2(9c+7)(9c-7)$

Answer:

$2(9c+7)(9c-7)$