Answer
$$(y^3+x^4)^3=x^{12}+3x^8y^3+3x^4y^6+y^9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(y^3+x^4)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}y^9+3x^4y^6+3x^8y^3+x^{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^{12}+3x^8y^3+3x^4y^6+y^9\end{aligned} $$ | |
| ① | Find $ \left(y^3+x^4\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = y^3 $ and $ B = x^4 $. $$ \left(y^3+x^4\right)^3 = \left( y^3 \right)^3+3 \cdot \left( y^3 \right)^2 \cdot x^4 + 3 \cdot y^3 \cdot \left( x^4 \right)^2+\left( x^4 \right)^3 = y^9+3x^4y^6+3x^8y^3+x^{12} $$ |
| ② | Combine like terms: $$ x^{12}+3x^8y^3+3x^4y^6+y^9 = x^{12}+3x^8y^3+3x^4y^6+y^9 $$ |
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