Chapter 1 - Review - Exercises: 41

$x^{2}(x-2)+x(x-2)^{2}=2x(x-2)(x-1)$

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: $...=2x(x-2)(x-1)$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.