High School

Simplify [tex]\left(7x^2+3\right)\left(7x^2-3\right)[/tex] using the difference of squares formula.

A) [tex]49x^4-9[/tex]
B) [tex]49x^2-9[/tex]
C) [tex]7x^4-9[/tex]
D) [tex]7x^2-1[/tex]

Answer :

To simplify [tex]\((7x^2 + 3)(7x^2 - 3)\)[/tex] using the difference of squares formula, let's follow these steps:

1. Understand the Difference of Squares Formula:

The difference of squares formula is:
[tex]\((a + b)(a - b) = a^2 - b^2\)[/tex]

Here, the expression fits this pattern where:
- [tex]\(a = 7x^2\)[/tex]
- [tex]\(b = 3\)[/tex]

2. Apply the Formula:

Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula:

[tex]\[
(7x^2 + 3)(7x^2 - 3) = (7x^2)^2 - 3^2
\][/tex]

3. Calculate Each Square:

- [tex]\((7x^2)^2 = 49x^4\)[/tex]
- [tex]\(3^2 = 9\)[/tex]

4. Simplify:

Substitute these values back into the expression:

[tex]\[
49x^4 - 9
\][/tex]

Thus, the simplified form of [tex]\((7x^2 + 3)(7x^2 - 3)\)[/tex] is [tex]\(\boxed{49x^4 - 9}\)[/tex], which matches option A.