Answer
(a) B
(b) C
(c) A
Work Step by Step
Check each factorization by using FOIL:
A. (3 - 2x)(9 + 6x + 4$x^{2}$) = 3(9) + 3(6x) + 3(4$x^{2}$) - 2x(9) - 2x(6x) - 2x(4$x^{2}$) = 27 + 18x + 12$x^{2}$ - 18x - 12$x^{2}$ - 8$x^{3}$ = 27 - 8$x^{3}$
B. (2x - 3)(4$x^{2}$ + 6x + 9) = 2x(4$x^{2}$) + 2x(6x) + 2x(9) - 3(4$x^{2}$) - 3(6x) - 3(9) = 8$x^{3}$ + 12$x^{2}$ + 18x - 12$x^{2}$ - 18x - 27 = 8$x^{3}$ - 27
C. (2x + 3)(4$x^{2}$ - 6x + 9) = 2x(4$x^{2}$) + 2x(-6x) + 2x(9) + 3(4$x^{2}$) + 3(-6x) + 3(9) = 8$x^{3}$ - 12$x^{2}$ + 18x + 12$x^{2}$ - 18x + 27 = 8$x^{3}$ + 27
