Question

Select the two binomials that are factors of 81x^2 - 36.
09x -6
09x+6
09x +12
09x-3

Answer 1

To factor the expression \(81x^2 - 36\), we first observe that it is a difference of squares. We can rewrite it in the form \(a^2 - b^2\), where:

- \(a^2 = (9x)^2\) (since \(81x^2 = (9x)^2\))
- \(b^2 = 6^2\) (since \(36 = 6^2\))

Thus, we can rewrite the expression as follows:

\[
81x^2 - 36 = (9x)^2 - 6^2
\]

Using the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\), we can factor our expression:

\[
81x^2 - 36 = (9x - 6)(9x + 6)
\]

Now we identify the two binomials that are factors from the options given:

- \(09x - 6\) (or \(9x - 6\))
- \(09x + 6\) (or \(9x + 6\))
- \(09x + 12\)
- \(09x - 3\)

The two factors of \(81x^2 - 36\) are:

**1. \(9x - 6\)**
**2. \(9x + 6\)**

So the correct binomials are:

- \(9x - 6\)
- \(9x + 6\)