Answer
$x^{2}(x-2)+x(x-2)^{2}=2x(x-2)(x-1)$
Work Step by Step
$x^{2}(x-2)+x(x-2)^{2}$
Evaluate the product in the first term and the power in the second term:
$x^{2}(x-2)+x(x-2)^{2}=...$
$...=x^{3}-2x^{2}+x(x^{2}-4x+4)=...$
Evaluate the remaining product and simplify:
$...=x^{3}-2x^{2}+x^{3}-4x^{2}+4x=...$
$...=2x^{3}-6x^{2}+4x=...$
Take out common factor $2x$:
$...=2x(x^{2}-3x+2)=...$
Finally, factor the expression inside the parentheses to give a more simplified answer:
$...=2x(x-2)(x-1)$
