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Answer :
To simplify [tex]\((7x^2 + 3)(7x^2 - 3)\)[/tex] using the difference of squares formula, let's first understand the formula itself.
The difference of squares formula states that for any two numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
In this problem, we need to identify what [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are in the expression [tex]\((7x^2 + 3)(7x^2 - 3)\)[/tex]:
- [tex]\(a\)[/tex] is [tex]\(7x^2\)[/tex]
- [tex]\(b\)[/tex] is [tex]\(3\)[/tex]
Now let's apply the formula:
1. Calculate [tex]\(a^2\)[/tex]. Since [tex]\(a = 7x^2\)[/tex],
[tex]\[
a^2 = (7x^2)^2 = 49x^4
\][/tex]
2. Calculate [tex]\(b^2\)[/tex]. Since [tex]\(b = 3\)[/tex],
[tex]\[
b^2 = 3^2 = 9
\][/tex]
3. Apply the difference of squares formula:
[tex]\[
a^2 - b^2 = 49x^4 - 9
\][/tex]
Therefore, the simplified expression is [tex]\[49x^4 - 9\][/tex].
The correct answer is:
B) [tex]\(49x^4 - 9\)[/tex]
The difference of squares formula states that for any two numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
In this problem, we need to identify what [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are in the expression [tex]\((7x^2 + 3)(7x^2 - 3)\)[/tex]:
- [tex]\(a\)[/tex] is [tex]\(7x^2\)[/tex]
- [tex]\(b\)[/tex] is [tex]\(3\)[/tex]
Now let's apply the formula:
1. Calculate [tex]\(a^2\)[/tex]. Since [tex]\(a = 7x^2\)[/tex],
[tex]\[
a^2 = (7x^2)^2 = 49x^4
\][/tex]
2. Calculate [tex]\(b^2\)[/tex]. Since [tex]\(b = 3\)[/tex],
[tex]\[
b^2 = 3^2 = 9
\][/tex]
3. Apply the difference of squares formula:
[tex]\[
a^2 - b^2 = 49x^4 - 9
\][/tex]
Therefore, the simplified expression is [tex]\[49x^4 - 9\][/tex].
The correct answer is:
B) [tex]\(49x^4 - 9\)[/tex]
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