Question

1. $2x^2 - 32$

Explanation:

Step1: Factor out the common factor

First, we can factor out the greatest common factor of the two terms \(2x^2\) and \(-32\), which is \(2\). So we have:
\(2x^2 - 32 = 2(x^2 - 16)\)

Step2: Apply the difference of squares formula

The expression \(x^2 - 16\) is a difference of squares, since \(x^2\) is a square and \(16 = 4^2\). The difference of squares formula is \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = x\) and \(b = 4\), so we can factor \(x^2 - 16\) as \((x + 4)(x - 4)\).
Substituting back into the expression from Step 1, we get:
\(2(x^2 - 16)=2(x + 4)(x - 4)\)

Answer:

\(2(x + 4)(x - 4)\)