Answer:
a. 6x^3 - 24x^2 + 6x + 36
Step-by-step explanation:
These are expanded using the distributive property, which is also used for collecting terms.
(2x - 6)(3x2 - 3x - 6) = 2x(3x^2 - 3x - 6) - 6(3x^2 - 3x - 6)
= 6x^3 -6x^2 -12x -18x^2 +18x +36
= 6x^3 +(-6-18)x^2 +(-12 +18)x +36
= 6x^3 -24x^2 +6x +36 . . . . . . matches selection A
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Comment on strategy
For multiple-choice questions, it often works well to find a way to identify a viable answer with the minimum amount of work. Comparing these answer choices, you can see that determining the correct values of the x-term and the constant term will let you pick the right choice.
The constant term is easy, because it is simply the product of the constants (-6)(-6) = 36. This narrows the choices to A and C.
The x-term will be the sum of products of x-terms and constants:
2x(-6) +(-6)(-3x) = -6(2x-3x) = -6(-x) = 6x
This narrows the choices to A alone.
