1. Problem: Factor out the common binomial factor $(x+2)$ from an expression. 2. Suppose the expression is of the form $(x+2)(ax+b) + (x+2)(cx+d)$. Our goal is to factor $(x+2)$ out. 3. Factor out $(x+2)$: $$ (x+2)(ax+b) + (x+2)(cx+d) = (x+2) [(ax+b) + (cx+d)] $$ 4. Simplify inside the bracket: $$ (ax+b) + (cx+d) = (a+c)x + (b+d) $$ 5. The fully factored form is: $$ (x+2)((a+c)x + (b+d)) $$ This shows the process of factoring out a common binomial factor $(x+2)$ by grouping and summing the remaining terms.