#### Answer

$3x^2+16xy-35y^2$

#### Work Step by Step

To find our answer, we use the FOIL method to multiply these two factors together. To use the FOIL method, we multiply the first term from each binomial, the first term from the first binomial and the last term from the second binomial, the last term of the first binomial and the first term of the second binomial, and the last terms of each binomial. We then find the sum of these product and combine the like terms to get our answer.
When we apply this method to $(x+7y)(3x-5y)$, we get the answer $3x^2+16xy-35y^2$.