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Answer :
To simplify the expression [tex]\((7x^2 + 3)(7x^2 - 3)\)[/tex] using the difference of squares formula, we need to recognize that it fits the form [tex]\((a + b)(a - b) = a^2 - b^2\)[/tex].
Here’s how you can apply this formula step by step:
1. Identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- In the given expression [tex]\((7x^2 + 3)(7x^2 - 3)\)[/tex], we can see that:
- [tex]\(a = 7x^2\)[/tex]
- [tex]\(b = 3\)[/tex]
2. Apply the difference of squares formula:
- According to the formula [tex]\((a + b)(a - b) = a^2 - b^2\)[/tex], we substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] with the identified values:
[tex]\[
(7x^2)^2 - 3^2
\][/tex]
3. Calculate [tex]\(a^2\)[/tex] and [tex]\(b^2\)[/tex]:
- [tex]\(a^2 = (7x^2)^2 = 49x^4\)[/tex]
- [tex]\(b^2 = 3^2 = 9\)[/tex]
4. Substitute back into the formula:
- So, the expression becomes:
[tex]\[
49x^4 - 9
\][/tex]
Therefore, the simplified expression is [tex]\(49x^4 - 9\)[/tex]. So, the correct answer is A) [tex]\(49x^4 - 9\)[/tex].
Here’s how you can apply this formula step by step:
1. Identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- In the given expression [tex]\((7x^2 + 3)(7x^2 - 3)\)[/tex], we can see that:
- [tex]\(a = 7x^2\)[/tex]
- [tex]\(b = 3\)[/tex]
2. Apply the difference of squares formula:
- According to the formula [tex]\((a + b)(a - b) = a^2 - b^2\)[/tex], we substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] with the identified values:
[tex]\[
(7x^2)^2 - 3^2
\][/tex]
3. Calculate [tex]\(a^2\)[/tex] and [tex]\(b^2\)[/tex]:
- [tex]\(a^2 = (7x^2)^2 = 49x^4\)[/tex]
- [tex]\(b^2 = 3^2 = 9\)[/tex]
4. Substitute back into the formula:
- So, the expression becomes:
[tex]\[
49x^4 - 9
\][/tex]
Therefore, the simplified expression is [tex]\(49x^4 - 9\)[/tex]. So, the correct answer is A) [tex]\(49x^4 - 9\)[/tex].
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