Question
Answer
$$2(x-4)^3+48=2x^3-24x^2+96x-80$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-4)^3+48& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^3-12x^2+48x-64)+48 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^3-24x^2+96x-128+48 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3-24x^2+96x-80\end{aligned} $$ | |
| ① | Find $ \left(x-4\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = x $ and $ B = 4 $. $$ \left(x-4\right)^3 = x^3-3 \cdot x^2 \cdot 4 + 3 \cdot x \cdot 4^2-4^3 = x^3-12x^2+48x-64 $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x^3-12x^2+48x-64\right) $ $$ \color{blue}{2} \cdot \left( x^3-12x^2+48x-64\right) = 2x^3-24x^2+96x-128 $$ |
| ③ | Combine like terms: $$ 2x^3-24x^2+96x \color{blue}{-128} + \color{blue}{48} = 2x^3-24x^2+96x \color{blue}{-80} $$ |
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