Question
Answer
$$(y-4x)^3=-64x^3+48x^2y-12xy^2+y^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(y-4x)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}y^3-12xy^2+48x^2y-64x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-64x^3+48x^2y-12xy^2+y^3\end{aligned} $$ | |
| ① | Find $ \left(y-4x\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = y $ and $ B = 4x $. $$ \left(y-4x\right)^3 = y^3-3 \cdot y^2 \cdot 4x + 3 \cdot y \cdot \left( 4x \right)^2-\left( 4x \right)^3 = y^3-12xy^2+48x^2y-64x^3 $$ |
| ② | Combine like terms: $$ -64x^3+48x^2y-12xy^2+y^3 = -64x^3+48x^2y-12xy^2+y^3 $$ |
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