Question
49x^2-144 factored
Answers
GPT-4o mini
To factor the expression \(49x^2 - 144\), you can recognize that it takes the form of a difference of squares. The difference of squares formula is:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify:
- \(a^2 = 49x^2\) which means \(a = 7x\)
- \(b^2 = 144\) which means \(b = 12\)
Now, applying the difference of squares formula:
\[
49x^2 - 144 = (7x)^2 - 12^2 = (7x - 12)(7x + 12)
\]
Thus, the factored form of \(49x^2 - 144\) is:
\[
(7x - 12)(7x + 12)
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify:
- \(a^2 = 49x^2\) which means \(a = 7x\)
- \(b^2 = 144\) which means \(b = 12\)
Now, applying the difference of squares formula:
\[
49x^2 - 144 = (7x)^2 - 12^2 = (7x - 12)(7x + 12)
\]
Thus, the factored form of \(49x^2 - 144\) is:
\[
(7x - 12)(7x + 12)
\]