Question
Answer
$$9\cdot\dfrac{x^2}{4}(8x-8)=\dfrac{72x^3-72x^2}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9 \cdot \frac{x^2}{4}(8x-8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9x^2}{4}(8x-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{72x^3-72x^2}{4}\end{aligned} $$ | |
| ① | Multiply $9$ by $ \dfrac{x^2}{4} $ to get $ \dfrac{ 9x^2 }{ 4 } $. Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 9 \cdot \frac{x^2}{4} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{x^2}{4} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x^2 }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^2 }{ 4 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{9x^2}{4} $ by $ 8x-8 $ to get $ \dfrac{ 72x^3-72x^2 }{ 4 } $. Step 1: Write $ 8x-8 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{9x^2}{4} \cdot 8x-8 & \xlongequal{\text{Step 1}} \frac{9x^2}{4} \cdot \frac{8x-8}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9x^2 \cdot \left( 8x-8 \right) }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 72x^3-72x^2 }{ 4 } \end{aligned} $$ |
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