Question
Answer
$$(3y+x)^3=x^3+9x^2y+27xy^2+27y^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3y+x)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}27y^3+27xy^2+9x^2y+x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3+9x^2y+27xy^2+27y^3\end{aligned} $$ | |
| ① | Find $ \left(3y+x\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 3y $ and $ B = x $. $$ \left(3y+x\right)^3 = \left( 3y \right)^3+3 \cdot \left( 3y \right)^2 \cdot x + 3 \cdot 3y \cdot x^2+x^3 = 27y^3+27xy^2+9x^2y+x^3 $$ |
| ② | Combine like terms: $$ x^3+9x^2y+27xy^2+27y^3 = x^3+9x^2y+27xy^2+27y^3 $$ |
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