Question
Answer
$$\dfrac{50r^2+20r+2}{r^2}\dfrac{r^3+5r^2}{2}=\dfrac{50r^5+270r^4+102r^3+10r^2}{2r^2}$$
Explanation
| $$ \begin{aligned}\frac{50r^2+20r+2}{r^2}\frac{r^3+5r^2}{2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{50r^5+270r^4+102r^3+10r^2}{2r^2}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{50r^2+20r+2}{r^2} $ by $ \dfrac{r^3+5r^2}{2} $ to get $ \dfrac{50r^5+270r^4+102r^3+10r^2}{2r^2} $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{50r^2+20r+2}{r^2} \cdot \frac{r^3+5r^2}{2} & \xlongequal{\text{Step 1}} \frac{ \left( 50r^2+20r+2 \right) \cdot \left( r^3+5r^2 \right) }{ r^2 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 50r^5+250r^4+20r^4+100r^3+2r^3+10r^2 }{ 2r^2 } = \frac{50r^5+270r^4+102r^3+10r^2}{2r^2} \end{aligned} $$ |
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