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