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