Question
Answer
$$\dfrac{1}{2}\cdot7x^2(4x^3+18)=\dfrac{28x^5+126x^2}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{2}\cdot7x^2(4x^3+18)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7x^2}{2}(4x^3+18) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{28x^5+126x^2}{2}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{2} $ by $ 7x^2 $ to get $ \dfrac{ 7x^2 }{ 2 } $. Step 1: Write $ 7x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{2} \cdot 7x^2 & \xlongequal{\text{Step 1}} \frac{1}{2} \cdot \frac{7x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot 7x^2 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^2 }{ 2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{7x^2}{2} $ by $ 4x^3+18 $ to get $ \dfrac{ 28x^5+126x^2 }{ 2 } $. Step 1: Write $ 4x^3+18 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{7x^2}{2} \cdot 4x^3+18 & \xlongequal{\text{Step 1}} \frac{7x^2}{2} \cdot \frac{4x^3+18}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7x^2 \cdot \left( 4x^3+18 \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 28x^5+126x^2 }{ 2 } \end{aligned} $$ |
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