Question

(1)^2 = 1 (5x - 1)(3x + 1) (4) 9. 100x^2 - 36 10.

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of \(100x^2\) and \(36\). The GCF of \(100\) and \(36\) is \(4\). So, factor out \(4\):
\(100x^2 - 36 = 4(25x^2 - 9)\)

Step2: Apply the difference of squares

Notice that \(25x^2 - 9\) is a difference of squares, since \(25x^2=(5x)^2\) and \(9 = 3^2\). The formula for the difference of squares is \(a^2 - b^2=(a - b)(a + b)\). Here, \(a = 5x\) and \(b = 3\), so:
\(25x^2 - 9=(5x - 3)(5x + 3)\)

Step3: Combine the factors

Substitute the factored form of \(25x^2 - 9\) back into the expression from Step 1:
\(4(25x^2 - 9)=4(5x - 3)(5x + 3)\)

Answer:

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