Answer
$$(x^2+2x-2)^3=x^6+6x^5+6x^4-16x^3-12x^2+24x-8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+2x-2)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^6+6x^5+6x^4-16x^3-12x^2+24x-8\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+2x-2}\right) $ by each term in $ \left( x^2+2x-2\right) $. $$ \left( \color{blue}{x^2+2x-2}\right) \cdot \left( x^2+2x-2\right) = x^4+2x^3-2x^2+2x^3+4x^2-4x-2x^2-4x+4 $$ |
| ② | Combine like terms: $$ x^4+ \color{blue}{2x^3} \color{red}{-2x^2} + \color{blue}{2x^3} + \color{green}{4x^2} \color{orange}{-4x} \color{green}{-2x^2} \color{orange}{-4x} +4 = x^4+ \color{blue}{4x^3} \color{orange}{-8x} +4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^4+4x^3-8x+4}\right) $ by each term in $ \left( x^2+2x-2\right) $. $$ \left( \color{blue}{x^4+4x^3-8x+4}\right) \cdot \left( x^2+2x-2\right) = \\ = x^6+2x^5-2x^4+4x^5+8x^4-8x^3-8x^3-16x^2+16x+4x^2+8x-8 $$ |
| ④ | Combine like terms: $$ x^6+ \color{blue}{2x^5} \color{red}{-2x^4} + \color{blue}{4x^5} + \color{red}{8x^4} \color{green}{-8x^3} \color{green}{-8x^3} \color{orange}{-16x^2} + \color{blue}{16x} + \color{orange}{4x^2} + \color{blue}{8x} -8 = \\ = x^6+ \color{blue}{6x^5} + \color{red}{6x^4} \color{green}{-16x^3} \color{orange}{-12x^2} + \color{blue}{24x} -8 $$ |
This page was created using
Simplify polynomials calculator