Final answer:
To multiply the algebraic expressions (5u+7v)(u-6v) using the FOIL method, we first multiply the First terms, then the Outer terms, the Inner terms, and finally the Last terms. After combining the terms, the final answer is 5u^2 - 30uv + 7uv - 42v^2.
Step-by-step explanation:
To multiply the algebraic expressions (5u+7v)(u-6v) using the FOIL method, we need to multiply the First terms, the Outer terms, the Inner terms, and finally the Last terms.
The First terms are 5u multiplied by u, which equals 5u^2.
The Outer terms are 5u multiplied by -6v, which equals -30uv.
The Inner terms are 7v multiplied by u, which equals 7uv.
And the Last terms are 7v multiplied by -6v, which equals -42v^2.
Now, we can combine these four terms to get the final answer: 5u^2 - 30uv + 7uv - 42v^2.