To find the product of the binomials [tex]\((2x - 5)(2x + 5)\)[/tex], we'll expand the expression step-by-step using the distributive property, commonly known as the FOIL method (First, Outer, Inner, Last).
Given:
[tex]\[
(2x - 5)(2x + 5)
\][/tex]
1. First: Multiply the first terms in each binomial:
[tex]\[
2x \cdot 2x = 4x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
2x \cdot 5 = 10x
\][/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-5 \cdot 5 = -25
\][/tex]
Now, combine all these results:
[tex]\[
4x^2 + 10x - 10x - 25
\][/tex]
Next, simplify the expression by combining like terms:
[tex]\[
4x^2 + 10x - 10x - 25 = 4x^2 - 25
\][/tex]
Thus, the product of [tex]\((2x - 5)(2x + 5)\)[/tex] is:
[tex]\[
4x^2 - 25
\][/tex]
So, the correct answer is:
A. [tex]\(4x^2 - 25\)[/tex]
