Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}24u^3-12 \cdot \frac{u^2}{3}u^{224}\frac{u^3}{3}u^{212}\frac{u^2}{3}u^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}24u^3-\frac{12u^2}{3}u^{224}\frac{u^3}{3}u^{212}\frac{u^2}{3}u^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}24u^3-\frac{12u^{226}}{3}\frac{u^3}{3}u^{212}\frac{u^2}{3}u^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}24u^3-\frac{12u^{229}}{9}u^{212}\frac{u^2}{3}u^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}24u^3-\frac{12u^{441}}{9}\frac{u^2}{3}u^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}24u^3-\frac{12u^{443}}{27}u^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}24u^3-\frac{12u^{445}}{27} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{-12u^{445}+648u^3}{27}\end{aligned} $$ | |
| ① | Multiply $12$ by $ \dfrac{u^2}{3} $ to get $ \dfrac{ 12u^2 }{ 3 } $. Step 1: Write $ 12 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 12 \cdot \frac{u^2}{3} & \xlongequal{\text{Step 1}} \frac{12}{\color{red}{1}} \cdot \frac{u^2}{3} \xlongequal{\text{Step 2}} \frac{ 12 \cdot u^2 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12u^2 }{ 3 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{12u^2}{3} $ by $ u^{224} $ to get $ \dfrac{ 12u^{226} }{ 3 } $. Step 1: Write $ u^{224} $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{12u^2}{3} \cdot u^{224} & \xlongequal{\text{Step 1}} \frac{12u^2}{3} \cdot \frac{u^{224}}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 12u^2 \cdot u^{224} }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12u^{226} }{ 3 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{12u^{226}}{3} $ by $ \dfrac{u^3}{3} $ to get $ \dfrac{ 12u^{229} }{ 9 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{12u^{226}}{3} \cdot \frac{u^3}{3} & \xlongequal{\text{Step 1}} \frac{ 12u^{226} \cdot u^3 }{ 3 \cdot 3 } \xlongequal{\text{Step 2}} \frac{ 12u^{229} }{ 9 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{12u^{229}}{9} $ by $ u^{212} $ to get $ \dfrac{ 12u^{441} }{ 9 } $. Step 1: Write $ u^{212} $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{12u^{229}}{9} \cdot u^{212} & \xlongequal{\text{Step 1}} \frac{12u^{229}}{9} \cdot \frac{u^{212}}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 12u^{229} \cdot u^{212} }{ 9 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12u^{441} }{ 9 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{12u^{441}}{9} $ by $ \dfrac{u^2}{3} $ to get $ \dfrac{ 12u^{443} }{ 27 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{12u^{441}}{9} \cdot \frac{u^2}{3} & \xlongequal{\text{Step 1}} \frac{ 12u^{441} \cdot u^2 }{ 9 \cdot 3 } \xlongequal{\text{Step 2}} \frac{ 12u^{443} }{ 27 } \end{aligned} $$ |
| ⑥ | Multiply $ \dfrac{12u^{443}}{27} $ by $ u^2 $ to get $ \dfrac{ 12u^{445} }{ 27 } $. Step 1: Write $ u^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{12u^{443}}{27} \cdot u^2 & \xlongequal{\text{Step 1}} \frac{12u^{443}}{27} \cdot \frac{u^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 12u^{443} \cdot u^2 }{ 27 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12u^{445} }{ 27 } \end{aligned} $$ |
| ⑦ | Subtract $ \dfrac{12u^{445}}{27} $ from $ 24u^3 $ to get $ \dfrac{ \color{purple}{ -12u^{445}+648u^3 } }{ 27 }$. Step 1: Write $ 24u^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |