Question

what is the completely factored form of $8x^2 - 50$?

• $2(x + 5)(x - 5)$
• $2(2x - 5)(2x - 5)$
• $2(2x + 5)(2x + 5)$
• $2(2x + 5)(2x - 5)$

Explanation:

Step1: Factor out GCF

First, identify the greatest common factor (GCF) of $8x^2$ and $50$, which is 2.
$8x^2 - 50 = 2(4x^2 - 25)$

Step2: Factor difference of squares

Notice that $4x^2 - 25$ is a difference of squares, where $4x^2=(2x)^2$ and $25=5^2$. Use the difference of squares formula $a^2 - b^2=(a+b)(a-b)$.
$4x^2 - 25 = (2x + 5)(2x - 5)$

Step3: Combine factors

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

Answer:

D. $2(2x + 5)(2x - 5)$