What is the product of [tex]\((3x + 5)(3x - 5)\)[/tex]?

A. [tex]\(6x^2 + 30x - 25\)[/tex]
B. [tex]\(6x^2 - 25\)[/tex]
C. [tex]\(9x^2 - 25\)[/tex]
D. [tex]\(9x^2 + 30x - 25\)[/tex]



Answer :

To find the product of [tex]\((3x + 5)(3x - 5)\)[/tex], we can use the difference of squares formula. The difference of squares states that:

[tex]\[ (a + b)(a - b) = a^2 - b^2 \][/tex]

In this case, let's identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex] in our expression:

- [tex]\(a = 3x\)[/tex]
- [tex]\(b = 5\)[/tex]

Now, applying the difference of squares formula:

[tex]\[ (3x + 5)(3x - 5) = (3x)^2 - 5^2 \][/tex]

Next, we calculate each part:

[tex]\[ (3x)^2 = (3x) \cdot (3x) = 9x^2 \][/tex]

[tex]\[ 5^2 = 5 \cdot 5 = 25 \][/tex]

Putting it all together:

[tex]\[ (3x + 5)(3x - 5) = 9x^2 - 25 \][/tex]

So, the product of [tex]\((3x + 5)(3x - 5)\)[/tex] is:

[tex]\[ 9x^2 - 25 \][/tex]

Therefore, the correct answer is:

C. [tex]\(9x^2 - 25\)[/tex]