1. **Stating the problem:** We want to factor a common binomial, which means expressing it as a product of simpler expressions. 2. **Formula and rules:** When factoring a binomial, look for common factors in each term. The general approach is to use the distributive property in reverse: $$a b + a c = a(b + c)$$ where $a$ is the common factor. 3. **Step-by-step explanation:** - Identify the greatest common factor (GCF) of the terms. - Factor out the GCF from each term. - Write the expression as the product of the GCF and the remaining binomial. 4. **Example:** Factor the binomial $$6x + 9$$. - The GCF of 6 and 9 is 3. - Factor out 3: $$6x + 9 = 3(2x + 3)$$. 5. **Summary:** Factoring a common binomial involves finding the GCF and rewriting the expression as a product of the GCF and the simplified binomial inside parentheses.