Question
Answer
$$(a+b)^3-3a^2b-3ab^2=a^3+b^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a+b)^3-3a^2b-3ab^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}a^3+3a^2b+3ab^2+b^3-3a^2b-3ab^2 \xlongequal{ } \\[1 em] & \xlongequal{ }a^3+ \cancel{3a^2b}+ \cancel{3ab^2}+b^3 -\cancel{3a^2b} -\cancel{3ab^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^3+b^3\end{aligned} $$ | |
| ① | Find $ \left(a+b\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = a $ and $ B = b $. $$ \left(a+b\right)^3 = a^3+3 \cdot a^2 \cdot b + 3 \cdot a \cdot b^2+b^3 = a^3+3a^2b+3ab^2+b^3 $$ |
| ② | Combine like terms: $$ a^3+ \, \color{blue}{ \cancel{3a^2b}} \,+ \, \color{green}{ \cancel{3ab^2}} \,+b^3 \, \color{blue}{ -\cancel{3a^2b}} \, \, \color{green}{ -\cancel{3ab^2}} \, = a^3+b^3 $$ |
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