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

1. Problem Description

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

2. Solution Steps

The given expression is $7x(a+8b) + (a+8b)$.

We observe that the term $(a+8b)$ is common to both terms in the expression.

We can factor out $(a+8b)$ from both terms.

$7x(a+8b) + (a+8b) = (7x + 1)(a+8b)$

3. Final Answer

$(7x+1)(a+8b)$