Answer
$$-\frac{32}{3}x(-\frac{x}{4}+1)^3=\frac{32x}{3}(-\frac{x}{4}+1)^3$$
Explanation
| $$ \begin{aligned}-\frac{32}{3}x(-\frac{x}{4}+1)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{32x}{3}(-\frac{x}{4}+1)^3\end{aligned} $$ | |
| ① | Multiply $ \dfrac{32}{3} $ by $ x $ to get $ \dfrac{ 32x }{ 3 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{32}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{32}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 32 \cdot x }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 32x }{ 3 } \end{aligned} $$ |
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