Answer
$27x^{3}-54x^{2}+36x-8$
Work Step by Step
The standard form of a polynomial is
$a_{n}x^{n}+a_{n}x^{n-1}+\cdots+a_{1}x+a_{0}$
(written in order, highest degree first. If a term is missing, it means that the coefficient is 0)
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Use the perfect cube formula $(A-B)^{3}=A^{3}-3A^{2}B+3AB^{2}-B^{3}$ with $A=3x$ and $B=2$, to obtain:
$(3x-2)^{3}$
$=(3x)^{3}-3\cdot(3x)^{2}\cdot 2+3\cdot(3x)\cdot 2^{2}-2^{3}$
$=27x^{3}-6(9x^{2})+12(3x)-8$
$=27x^{3}-54x^{2}+36x-8$
