Question
Answer
$$(x+y)(x^2+2xy-y^3)=-xy^3-y^4+x^3+3x^2y+2xy^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+y)(x^2+2xy-y^3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3+2x^2y-xy^3+x^2y+2xy^2-y^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-xy^3-y^4+x^3+3x^2y+2xy^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+y}\right) $ by each term in $ \left( x^2+2xy-y^3\right) $. $$ \left( \color{blue}{x+y}\right) \cdot \left( x^2+2xy-y^3\right) = x^3+2x^2y-xy^3+x^2y+2xy^2-y^4 $$ |
| ② | Combine like terms: $$ x^3+ \color{blue}{2x^2y} -xy^3+ \color{blue}{x^2y} +2xy^2-y^4 = -xy^3-y^4+x^3+ \color{blue}{3x^2y} +2xy^2 $$ |
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