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:
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:
Final answer