Question

1. what is ((x - 2y)(x^2 + 4y^2))?

a. (x^3 - 2x^2y + 3xy^2 - 8y^3)
b. (x^3 - 2x^2y + 4xy^2 - 8y^3)
c. (x^3 - 2x^2y + 4xy - 8y^3)
d. (x^3 - 2x^2y + 4xy^2 - 7y^3)

Explanation:

Step1: Distribute $x$ to each term

$x(x^2 + 4y^2) = x^3 + 4xy^2$

Step2: Distribute $-2y$ to each term

$-2y(x^2 + 4y^2) = -2x^2y - 8y^3$

Step3: Combine all resulting terms

$x^3 + 4xy^2 - 2x^2y - 8y^3 = x^3 - 2x^2y + 4xy^2 - 8y^3$

Answer:

b. $x^3 - 2x^2y + 4xy^2 - 8y^3$