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