Question
Factor completely.
4, x, squared, minus, 81
4x
2
−81
4, x, squared, minus, 81
4x
2
−81
Answers
Answered by
GPT-4o mini
To factor the expression \(4x^2 - 81\), we can recognize that this is a difference of squares. The expression can be rewritten as follows:
\[
4x^2 - 81 = (2x)^2 - 9^2
\]
Using the difference of squares formula, \(a^2 - b^2 = (a - b)(a + b)\), we can apply it here:
- Let \(a = 2x\)
- Let \(b = 9\)
So, we have:
\[
(2x - 9)(2x + 9)
\]
Thus, the complete factorization of \(4x^2 - 81\) is:
\[
(2x - 9)(2x + 9)
\]
\[
4x^2 - 81 = (2x)^2 - 9^2
\]
Using the difference of squares formula, \(a^2 - b^2 = (a - b)(a + b)\), we can apply it here:
- Let \(a = 2x\)
- Let \(b = 9\)
So, we have:
\[
(2x - 9)(2x + 9)
\]
Thus, the complete factorization of \(4x^2 - 81\) is:
\[
(2x - 9)(2x + 9)
\]