Answer: The FOIL method (First, Outer, Inner, Last) is a mnemonic used to help solve and simplify multiplication problems by using the distributive property. To use FOIL, you simply multiply the first term of the first factor with the first term of the second factor, the outer terms of the two factors, the inner terms of the two factors, and the last terms of the two factors. Then, you add the results together to obtain the final answer.
For example, in the first problem, (a + b)(2a - 3b^2), we FOIL by first multiplying "a" and "2a": 2a^2. Next, we multiply "a" and "-3b^2": -3ab^2. Then, we multiply "b" and "2a": 2ab. Finally, we multiply "b" and "-3b^2": -3b^3. Now, we add the four results together to get the final answer: 2a^2 + (-3b^2 + 2b)a - 3b^3.
a. (a + b)(2a - 3b^2) = 2a^2 - 3ab^2 + 2ab - 3b^3 = 2a^2 + (-3b^2 + 2b)a - 3b^3.
b. (k - 8)(4k + b) = 4k^2 + bk - 32k - 8b = 4k^2 + (b - 32)k - 8b.
c. (7x^15)(2x + 2) = 14x^16 + 14x^15 = 14x^15 (x + 1).
d. (3ab - 1)(2ab + 6) = 6a^2 b^2 + 2ab - 3ab + 6 - 2ab = 6a^2 b^2 + 4ab +
Explanation: