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