Question

factor the following expression completely.

$2x^2 - 8$

a. $(2x + 2)(x - 2)$

b. $2(x^2 - 4)$

c. $2(x + 2)(x - 2)$

d. $2(x - 2)^2$

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(2x^2\) and \(8\) is \(2\). So, factor out \(2\) from the expression:
\(2x^2 - 8 = 2(x^2 - 4)\)

Step2: Factor the difference of squares

The expression \(x^2 - 4\) is a difference of squares, which can be factored using the formula \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = x\) and \(b = 2\), so:
\(x^2 - 4=(x + 2)(x - 2)\)

Step3: Combine the factors

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

Answer:

C. \(2(x + 2)(x - 2)\)