Question

1. $100x^2 - 36$

Explanation:

Step1: Factor out the GCF

Identify and factor out the greatest common factor of 100 and 36, which is 4.
$100x^2 - 36 = 4(25x^2 - 9)$

Step2: Apply difference of squares

Recognize $25x^2 - 9$ as a difference of squares ($a^2 - b^2 = (a-b)(a+b)$), where $a=5x$ and $b=3$.
$25x^2 - 9 = (5x - 3)(5x + 3)$

Step3: Combine factors

Substitute the factored form back into the expression from Step1.
$4(25x^2 - 9) = 4(5x - 3)(5x + 3)$

Answer:

$4(5x - 3)(5x + 3)$