Answer
(a) B
(b) C
(c) A
Work Step by Step
RECALL:
(i) $a^3-b^3 = (a-b)(a^2+ab+b^2)$
(ii) $a^3+b^3=(a+b)(a^2-ab+b^2)$
(a) $8x^3-27=(2x)^2-3^2$
Thus, using the formula in (1) above gives:
$8x^3-27
\\=(2x)^3-3^3
\\=(2x-3)[(2x)^2+(2x)(3)+3^2]
\\=(2x-3)(4x^2+6x+9)$
Thus, the answer is B.
(b) $8x^3+27=(2x)^2+3^2$
Thus, using the formula in (2) above gives:
$8x^3+27
\\=(2x)^3+3^3
\\=(2x+3)[(2x)^2-(2x)(3)+3^2]
\\=(2x+3)(4x^2-6x+9)$
Thus, the answer is C.
(c) $27 - 8x^3=3^3-(2x)^3$
Thus, using the formula in (1) above gives:
$27-8x^3
\\=3^3-(2x)^3
\\=(3-2x)[3^2+(3)(2x)+(2x)^2]
\\=(3-2x)(9+6x+4x^2)$
Thus, the answer is A.
