Answer
$(x-2)^3=x^3-6x^2+12x-8$.
Work Step by Step
The given expression is
$(x-2)^3$
The formula for the cube of an algebraic expression is
$(a-b)^3=a^3-b^3-3a^2b+3ab^2$
Plug $a=x$ and $b=2$ into the formula.
$(x-2)^3=x^3-2^3-3(x)^2(2)+3(x)(2)^2$
Clear the parentheses.
$(x-2)^3=x^3-8-6x^2+12x$
Simplify.
$(x-2)^3=x^3-6x^2+12x-8$.
