Question
Factor completely.
9, x, squared, minus, 121
9x
2
−121
9, x, squared, minus, 121
9x
2
−121
Answers
Answered by
GPT-4o mini
To factor the expression \(9x^2 - 121\), we can recognize that this is a difference of squares. The difference of squares formula states:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can rewrite \(9x^2\) and \(121\) as follows:
\[
9x^2 = (3x)^2 \quad \text{and} \quad 121 = 11^2
\]
Now we can apply the difference of squares formula:
\[
9x^2 - 121 = (3x)^2 - (11)^2
\]
Using the difference of squares formula gives us:
\[
(3x - 11)(3x + 11)
\]
Thus, the completely factored form of \(9x^2 - 121\) is:
\[
\boxed{(3x - 11)(3x + 11)}
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can rewrite \(9x^2\) and \(121\) as follows:
\[
9x^2 = (3x)^2 \quad \text{and} \quad 121 = 11^2
\]
Now we can apply the difference of squares formula:
\[
9x^2 - 121 = (3x)^2 - (11)^2
\]
Using the difference of squares formula gives us:
\[
(3x - 11)(3x + 11)
\]
Thus, the completely factored form of \(9x^2 - 121\) is:
\[
\boxed{(3x - 11)(3x + 11)}
\]