The problem asks us to factor out the greatest common factor from the expression $7x(x+y) - 8(x+y)$.

1. Problem Description

The problem asks us to factor out the greatest common factor from the expression $7x(x+y) - 8(x+y)$.

2. Solution Steps

We need to identify the greatest common factor in the given expression $7x(x+y) - 8(x+y)$.

We can observe that the term $(x+y)$ is common to both terms $7x(x+y)$ and $8(x+y)$.

Therefore, we can factor out $(x+y)$ from the expression.

$7x(x+y) - 8(x+y) = (x+y)(7x - 8)$.

3. Final Answer

$(x+y)(7x-8)$