Question

Factor the expression below.
x^2-81
0(x+ 27)(x-3)
0(x+ (x+9)(x-9)
0(x- 9)(x-9)
0 (x-27)(x-3)

Answer 1

To factor the expression \(x^2 - 81\), we need to recognize that it is a difference of squares. The difference of squares can be factored using the formula:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In this case, we can rewrite \(x^2 - 81\) as:

\[
x^2 - 9^2
\]

Here, \(a = x\) and \(b = 9\). Therefore, using the difference of squares formula, we have:

\[
x^2 - 81 = (x - 9)(x + 9)
\]

So, the correct answer is:

\((x - 9)(x + 9)\)

However, it appears that there was a mix-up in your options; if you meant for the answer options to reflect that format, please clarify. The correct factors are \((x - 9)(x + 9)\).