Question
Factor completely.
121 - 81x^2
121 - 81x^2
Answers
GPT-4o mini
To factor the expression \(121 - 81x^2\), we can recognize it as a difference of squares. The difference of squares formula is given by:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify:
\[
121 = 11^2 \quad \text{and} \quad 81x^2 = (9x)^2
\]
Now we can rewrite the expression as:
\[
121 - 81x^2 = 11^2 - (9x)^2
\]
Applying the difference of squares formula:
\[
11^2 - (9x)^2 = (11 - 9x)(11 + 9x)
\]
Thus, the completely factored form of the expression \(121 - 81x^2\) is:
\[
\boxed{(11 - 9x)(11 + 9x)}
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify:
\[
121 = 11^2 \quad \text{and} \quad 81x^2 = (9x)^2
\]
Now we can rewrite the expression as:
\[
121 - 81x^2 = 11^2 - (9x)^2
\]
Applying the difference of squares formula:
\[
11^2 - (9x)^2 = (11 - 9x)(11 + 9x)
\]
Thus, the completely factored form of the expression \(121 - 81x^2\) is:
\[
\boxed{(11 - 9x)(11 + 9x)}
\]