Question
Factor completely.
9x^2 - 1
9x^2 - 1
Answers
GPT-4o mini
To factor the expression \( 9x^2 - 1 \), we can recognize that it is a difference of squares. The difference of squares formula states that:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify:
\[
a^2 = (3x)^2 \quad \text{and} \quad b^2 = 1^2
\]
Thus, we can rewrite the expression \( 9x^2 - 1 \) as:
\[
(3x)^2 - 1^2
\]
Using the difference of squares formula:
\[
9x^2 - 1 = (3x - 1)(3x + 1)
\]
So, the completely factored form of \( 9x^2 - 1 \) is:
\[
(3x - 1)(3x + 1)
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify:
\[
a^2 = (3x)^2 \quad \text{and} \quad b^2 = 1^2
\]
Thus, we can rewrite the expression \( 9x^2 - 1 \) as:
\[
(3x)^2 - 1^2
\]
Using the difference of squares formula:
\[
9x^2 - 1 = (3x - 1)(3x + 1)
\]
So, the completely factored form of \( 9x^2 - 1 \) is:
\[
(3x - 1)(3x + 1)
\]