Question

find the product of each binomial and trinomial.

1. $(5 + a)(5a^{2} - 5a - 5) = $
2. $(3 - b)(2b^{2} + 3b - 4) = $

Explanation:

Step1: Distribute binomial to trinomial (Q18)

$(5+a)(5a^2 - 5a - 5) = 5(5a^2 - 5a - 5) + a(5a^2 - 5a - 5)$

Step2: Expand each term (Q18)

$= 25a^2 - 25a - 25 + 5a^3 - 5a^2 - 5a$

Step3: Combine like terms (Q18)

$= 5a^3 + (25a^2 - 5a^2) + (-25a - 5a) - 25 = 5a^3 + 20a^2 - 30a - 25$

Step4: Distribute binomial to trinomial (Q19)

$(3 - b)(2b^2 + 3b - 4) = 3(2b^2 + 3b - 4) - b(2b^2 + 3b - 4)$

Step5: Expand each term (Q19)

$= 6b^2 + 9b - 12 - 2b^3 - 3b^2 + 4b$

Step6: Combine like terms (Q19)

$= -2b^3 + (6b^2 - 3b^2) + (9b + 4b) - 12 = -2b^3 + 3b^2 + 13b - 12$

Answer:

1. $5a^3 + 20a^2 - 30a - 25$
2. $-2b^3 + 3b^2 + 13b - 12$