Final answer:
To multiply the binomials (10u-6v) and (u+7v), we use the distributive property and collect like terms.
Step-by-step explanation:
To multiply the binomials (10u-6v) and (u+7v), we will use the distributive property. We will multiply each term in the first binomial by each term in the second binomial, and then collect like terms.
So, (10u-6v)(u+7v) = 10u * u + 10u * 7v - 6v * u - 6v * 7v.
Simplifying, we get 10u^2 + 70uv - 6uv - 42v^2.
Finally, collecting like terms, the expression becomes 10u^2 + (70uv - 6uv) - 42v^2 = 10u^2 + 64uv - 42v^2.
Learn more about Multiplying Binomials