The problem asks us to factor out the greatest common factor from the expression $9x(x+y) - 8(x+y)$.

1. Problem Description

The problem asks us to factor out the greatest common factor from the expression $9x(x+y) - 8(x+y)$.

2. Solution Steps

The given expression is $9x(x+y) - 8(x+y)$. We can see that $(x+y)$ is a common factor in both terms. We can factor it out:

$9x(x+y) - 8(x+y) = (x+y)(9x - 8)$

3. Final Answer

$(x+y)(9x-8)$