1. The problem is to explain and demonstrate the FOIL method for multiplying two binomials. 2. FOIL stands for First, Outer, Inner, Last, which are the pairs of terms you multiply in each binomial. 3. Suppose we have two binomials: $ (a + b)(c + d) $. 4. Using FOIL, multiply: - First: $a \times c = ac$ - Outer: $a \times d = ad$ - Inner: $b \times c = bc$ - Last: $b \times d = bd$ 5. Add all these products together: $$ ac + ad + bc + bd $$ 6. This is the expanded form of the product of the two binomials. 7. Example: Multiply $ (x + 3)(x + 5) $ using FOIL. - First: $x \times x = x^2$ - Outer: $x \times 5 = 5x$ - Inner: $3 \times x = 3x$ - Last: $3 \times 5 = 15$ 8. Add them: $$ x^2 + 5x + 3x + 15 $$ 9. Combine like terms: $$ x^2 + 8x + 15 $$ 10. So, $ (x + 3)(x + 5) = x^2 + 8x + 15 $. This method helps multiply binomials quickly and accurately.