Question
Factor 9a2−49 (1 point) Responses (3a−7)(3a−7) open paren 3 A minus 7 close paren times open paren 3 A minus 7 close paren (3a+7)(3a−7) open paren 3 A plus 7 close paren times open paren 3 A minus 7 close paren (3a+7)(3a+7) open paren 3 A plus 7 close paren times open paren 3 A plus 7 close paren Prime
Answers
GPT-4o mini
To factor \(9a^2 - 49\), we can recognize that this expression is a difference of squares. The difference of squares formula states that:
\[
x^2 - y^2 = (x - y)(x + y)
\]
In this case:
- \(x^2 = 9a^2\), so \(x = 3a\)
- \(y^2 = 49\), so \(y = 7\)
Now we can apply the difference of squares formula:
\[
9a^2 - 49 = (3a - 7)(3a + 7)
\]
Thus, the factored form of \(9a^2 - 49\) is:
\((3a - 7)(3a + 7)\)
So the correct response from the options you provided is:
\((3a + 7)(3a - 7)\)
\[
x^2 - y^2 = (x - y)(x + y)
\]
In this case:
- \(x^2 = 9a^2\), so \(x = 3a\)
- \(y^2 = 49\), so \(y = 7\)
Now we can apply the difference of squares formula:
\[
9a^2 - 49 = (3a - 7)(3a + 7)
\]
Thus, the factored form of \(9a^2 - 49\) is:
\((3a - 7)(3a + 7)\)
So the correct response from the options you provided is:
\((3a + 7)(3a - 7)\)