How do you factor #8x^3 - 36x^2 + 54x - 27#?

1 Answer
George C.
Sep 28, 2015

Notice that #8x^3 = (2x)^3# and #-27 = (-3)^3#, so is the answer #(2x-3)^3# ?

Multiply out #(2x-3)^3# and find that it is.

#8x^3-36x^2+54x-27 = (2x-3)^3#

Explanation:

In general, #(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3#

Putting #a=2x# and #b=-3# we find:

#(2x-3)^3 = (2x)^3 + 3(2x)^2(-3) + 3(2x)(-3)^2 + (-3)^3#

#=8x^3-36x^2+54x-27#

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