Question

multiple and collect like terms (2u+7v)(u+2v).

Answer 1

Multiply and collect like terms:

(2u+7v)(u+2v)

We'll use the distributive property and multiply each term of the first binomial by each term of the second binomial:

(2u)(u) + (2u)(2v) + (7v)(u) + (7v)(2v)

Now multiply each monomial individually:

$2u^2+4uv+7vu+14v^2$

Note we have the terms 4uv and 7vu. They are like terms because variables can be swapped applying the commutative property, thus

4uv+7uv = 11uv

The final result is:

$2u^2+11uv+14v^2$

Final answer