If $$8x^3 - 27y^3 = (Ax + By) (Cx^2 - Dy^2 + 6xy),$$ then $$(A + B + C - D)$$ is equal to:
$$8x^3 - 27y^3 = (Ax + By) (Cx^2 - Dy^2 + 6xy)$$
$$(2x)^3 - (3y)^3 = (2x - 3y)(4x^2 + 9y^2 + 6xy) =Â (Ax + By) (Cx^2 - Dy^2 + 6xy)$$
$$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$
by comparing,
A = 2
B = -3
C = 4
D = -9
$$(A + B + C - D)$$ = 2 - 3 + 4 +Â 9 = 12
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