To find the product of [tex]\((5x + 1)(5x - 1)\)[/tex], let's expand the expression using the distributive property (also known as the FOIL method, which stands for First, Outside, Inside, Last):
1. First: Multiply the first terms in each binomial:
[tex]\[ (5x) \cdot (5x) = 25x^2 \][/tex]
2. Outside: Multiply the outer terms in the binomials:
[tex]\[ (5x) \cdot (-1) = -5x \][/tex]
3. Inside: Multiply the inner terms in the binomials:
[tex]\[ 1 \cdot (5x) = 5x \][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[ 1 \cdot (-1) = -1 \][/tex]
Now, add all the products together:
[tex]\[ 25x^2 - 5x + 5x - 1 \][/tex]
Notice that the [tex]\(-5x\)[/tex] and [tex]\(5x\)[/tex] terms cancel each other out:
[tex]\[ 25x^2 - 1 \][/tex]
So, the correct product of [tex]\((5x + 1)(5x - 1)\)[/tex] is:
[tex]\[ 25x^2 - 1 \][/tex]
Therefore, the correct answer is:
D. [tex]\( 25x^2 - 1 \)[/tex]
