Question

factor completely.
$98u^2 - 288$

Explanation:

Step1: Factor out GCD

Find GCD of 98 and 288, which is 2.
$98u^2 - 288 = 2(49u^2 - 144)$

Step2: Recognize difference of squares

$49u^2=(7u)^2$, $144=12^2$. Use $a^2-b^2=(a-b)(a+b)$.
$49u^2 - 144 = (7u - 12)(7u + 12)$

Step3: Combine factors

Substitute back into the expression.
$2(49u^2 - 144) = 2(7u - 12)(7u + 12)$

Answer:

$2(7u - 12)(7u + 12)$