What is the product of [tex](2x - 5)(2x + 5)[/tex]?

A. [tex]4x^2 - 25[/tex]

B. [tex]4x^2 - 10[/tex]

C. [tex]4x^2 + 20x - 10[/tex]

D. [tex]4x^2 + 20x - 25[/tex]



Answer :

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]