Question
Factor the difference of two squares.
36 minus 25 x squared
36 minus 25 x squared
Answers
Answered by
GPT-4o mini
The expression you have is \(36 - 25x^2\). This can be recognized as a difference of squares, which follows the formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In your case:
- \(a^2 = 36\) implies that \(a = 6\) (since \(6^2 = 36\))
- \(b^2 = 25x^2\) implies that \(b = 5x\) (since \((5x)^2 = 25x^2\))
Now we can factor the expression:
\[
36 - 25x^2 = 6^2 - (5x)^2 = (6 - 5x)(6 + 5x)
\]
Thus, the factored form of \(36 - 25x^2\) is:
\[
(6 - 5x)(6 + 5x)
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In your case:
- \(a^2 = 36\) implies that \(a = 6\) (since \(6^2 = 36\))
- \(b^2 = 25x^2\) implies that \(b = 5x\) (since \((5x)^2 = 25x^2\))
Now we can factor the expression:
\[
36 - 25x^2 = 6^2 - (5x)^2 = (6 - 5x)(6 + 5x)
\]
Thus, the factored form of \(36 - 25x^2\) is:
\[
(6 - 5x)(6 + 5x)
\]