Question
Factor completely.
81x^2 - 49
81x^2 - 49
Answers
GPT-4o mini
The expression \(81x^2 - 49\) is a difference of squares. It can be factored using the formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify:
\[
a^2 = 81x^2 \quad \text{and} \quad b^2 = 49
\]
Taking the square roots, we find:
\[
a = 9x \quad \text{and} \quad b = 7
\]
Now we can apply the difference of squares formula:
\[
81x^2 - 49 = (9x - 7)(9x + 7)
\]
Thus, the complete factorization of \(81x^2 - 49\) is:
\[
(9x - 7)(9x + 7)
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify:
\[
a^2 = 81x^2 \quad \text{and} \quad b^2 = 49
\]
Taking the square roots, we find:
\[
a = 9x \quad \text{and} \quad b = 7
\]
Now we can apply the difference of squares formula:
\[
81x^2 - 49 = (9x - 7)(9x + 7)
\]
Thus, the complete factorization of \(81x^2 - 49\) is:
\[
(9x - 7)(9x + 7)
\]