1. **Stating the problem:** We want to understand how to find the product of two binomials. 2. **Formula and rule:** The product of two binomials $(a+b)(c+d)$ is found by applying the distributive property (also called FOIL method for binomials): $$ (a+b)(c+d) = ac + ad + bc + bd $$ This means you multiply each term in the first binomial by each term in the second binomial. 3. **Explanation:** FOIL stands for First, Outer, Inner, Last: - First: multiply the first terms $a \times c$ - Outer: multiply the outer terms $a \times d$ - Inner: multiply the inner terms $b \times c$ - Last: multiply the last terms $b \times d$ 4. **Example:** Multiply $(x+3)(x+5)$: $$ \begin{aligned} (x+3)(x+5) &= x \times x + x \times 5 + 3 \times x + 3 \times 5 \\ &= x^2 + 5x + 3x + 15 \\ &= x^2 + 8x + 15 \end{aligned} $$ 5. **Summary:** To multiply binomials, multiply each term in the first by each term in the second, then combine like terms to simplify the expression.