Question

select two binomials that are factors 64x^2 - 36

8x - 3
8x + 12
8x - 6
8x + 6

Answer 1

To factor the expression \(64x^2 - 36\), we can start by recognizing that it is a difference of squares.

The general formula for factoring a difference of squares is:

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

In this case, we can identify:

- \(a^2 = 64x^2\) which means \(a = 8x\)
- \(b^2 = 36\) which means \(b = 6\) (since \(b^2 = 6^2\))

Now, applying the difference of squares formula, we get:

\[
64x^2 - 36 = (8x - 6)(8x + 6)
\]

Thus, the two binomials that are factors of \(64x^2 - 36\) are:

- \(8x - 6\)
- \(8x + 6\)

So, the correct choice is:

**8x - 6** and **8x + 6**.