Answer
$$(x+y)(x-y)(x+y)=x^3+x^2y-xy^2-y^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+y)(x-y)(x+y)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-xy+xy-y^2)(x+y) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-y^2)(x+y) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+x^2y-xy^2-y^3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+y}\right) $ by each term in $ \left( x-y\right) $. $$ \left( \color{blue}{x+y}\right) \cdot \left( x-y\right) = x^2 -\cancel{xy}+ \cancel{xy}-y^2 $$ |
| ② | Combine like terms: $$ x^2 \, \color{blue}{ -\cancel{xy}} \,+ \, \color{blue}{ \cancel{xy}} \,-y^2 = x^2-y^2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-y^2}\right) $ by each term in $ \left( x+y\right) $. $$ \left( \color{blue}{x^2-y^2}\right) \cdot \left( x+y\right) = x^3+x^2y-xy^2-y^3 $$ |
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Simplify Rational Expressions