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

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Answer 1 · 2015-09-28T06:28:22

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.

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

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

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

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

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

How do you factor 8x^3 - 36x^2 + 54x - 278x^3 - 36x^2 + 54x - 27?