Choose the correct simplification of the expression (2x - 6)(3x2 - 3x - 6). (4 points) Select one: a. 6x3 - 24x2 + 6x + 36 b. 6x3 - 24x2 + 6x - 36 c. 6x3 + 24x2 - 6x + 36 d. 6x3 - 24x2 + 6x + 12

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_____Comment on strategyFor 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) = 6xThis narrows the choices to A alone.