1. **State the problem:** We need to multiply the binomials $(3x - 4)(3x + 3)$ using the FOIL method. 2. **Recall the FOIL method:** FOIL stands for First, Outer, Inner, Last. It is a technique to multiply two binomials: - First: multiply the first terms in each binomial. - Outer: multiply the outer terms. - Inner: multiply the inner terms. - Last: multiply the last terms. 3. **Apply FOIL:** - First: $3x \times 3x = 9x^2$ - Outer: $3x \times 3 = 9x$ - Inner: $-4 \times 3x = -12x$ - Last: $-4 \times 3 = -12$ 4. **Combine like terms:** $$9x^2 + 9x - 12x - 12 = 9x^2 - 3x - 12$$ 5. **Final answer:** $$(3x - 4)(3x + 3) = 9x^2 - 3x - 12$$