Factor:9u^2+12uv+4^2

Answer 1

The given expression is a quadratic trinomial in the form of \( ax^2+bx+c \).

We have \( 9u^2+12uv+4^2 \).

The factors of 9u^2 are 3u and 3u.
The factors of 4^2 are 2 and 2.

Now, we need to find two numbers that multiply to \( 9u^2\cdot4^2 = 36u^2 \) and add up to \( 12uv \).

The numbers are 6u and 6u.

Therefore, we can factor the expression as follows:

\( 9u^2+12uv+4^2 = (3u+2)(3u+2) = (3u+2)^2 \)