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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.
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.
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