What is the completely factored form of [tex]8x^2 - 50[/tex]?

A. [tex]2(x + 5)(x - 5)[/tex]

B. [tex]2(2x - 5)(2x - 5)[/tex]

C. [tex]2(2x + 5)(2x + 5)[/tex]

D. [tex]2(2x + 5)(2x - 5)[/tex]



Answer :

To find the completely factored form of the quadratic expression [tex]\(8x^2 - 50\)[/tex], let's break it down step by step.

First, observe that [tex]\(8x^2 - 50\)[/tex] can be written as:
[tex]\[8x^2 - 50\][/tex]

We start by factoring out the greatest common factor (GCF). The GCF of the terms [tex]\(8x^2\)[/tex] and [tex]\(-50\)[/tex] is 2. So, we factor out 2 from the expression:
[tex]\[8x^2 - 50 = 2(4x^2 - 25)\][/tex]

Next, we focus on factoring the expression inside the parentheses: [tex]\(4x^2 - 25\)[/tex]. Notice that this is a difference of squares. Recall the difference of squares formula:
[tex]\[a^2 - b^2 = (a - b)(a + b)\][/tex]

We can apply this formula to [tex]\(4x^2 - 25\)[/tex], where [tex]\(4x^2\)[/tex] is [tex]\((2x)^2\)[/tex] and [tex]\(25\)[/tex] is [tex]\(5^2\)[/tex]:
[tex]\[4x^2 - 25 = (2x)^2 - 5^2\][/tex]

Using the difference of squares formula, we have:
[tex]\[4x^2 - 25 = (2x - 5)(2x + 5)\][/tex]

Finally, substituting back into our original factored form, we get:
[tex]\[8x^2 - 50 = 2(2x - 5)(2x + 5)\][/tex]

Thus, the completely factored form of [tex]\(8x^2 - 50\)[/tex] is:
[tex]\[2(2x - 5)(2x + 5)\][/tex]

So, the correct answer is:
[tex]\[2(2x+5)(2x-5)\][/tex]