Question

Factor Completely
36, u, squared, minus, 64
36u
2
−64

Answer 1

To factor the expression \( 36u^2 - 64 \), we can first recognize that it is a difference of squares. The expression can be written as:

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

We can then apply the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \).

Here, \( a = 6u \) and \( b = 8 \). Therefore, we can factor the expression as follows:

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

Next, we can simplify the factors further. We notice that both \( 6u - 8 \) and \( 6u + 8 \) have a common factor of 2.

Factoring out 2 gives:

\[
6u - 8 = 2(3u - 4)
\]
\[
6u + 8 = 2(3u + 4)
\]

Now substituting these back into our expression gives:

\[
36u^2 - 64 = (2(3u - 4))(2(3u + 4))
\]

This simplifies to:

\[
= 4(3u - 4)(3u + 4)
\]

Thus, the completely factored form of \( 36u^2 - 64 \) is:

\[
\boxed{4(3u - 4)(3u + 4)}
\]