Question
Answer
$$(a+b^3)^3=b^9+3ab^6+3a^2b^3+a^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a+b^3)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}a^3+3a^2b^3+3ab^6+b^9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}b^9+3ab^6+3a^2b^3+a^3\end{aligned} $$ | |
| ① | Find $ \left(a+b^3\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = a $ and $ B = b^3 $. $$ \left(a+b^3\right)^3 = a^3+3 \cdot a^2 \cdot b^3 + 3 \cdot a \cdot \left( b^3 \right)^2+\left( b^3 \right)^3 = a^3+3a^2b^3+3ab^6+b^9 $$ |
| ② | Combine like terms: $$ b^9+3ab^6+3a^2b^3+a^3 = b^9+3ab^6+3a^2b^3+a^3 $$ |
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