$$15y^2 \cdot \dfrac{y+3}{10}y^3(y+3)=\dfrac{15y^7+90y^6+135y^5}{10}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}15y^2\frac{y+3}{10}y^3(y+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{15y^3+45y^2}{10}y^3(y+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15y^6+45y^5}{10}(y+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15y^7+90y^6+135y^5}{10}\end{aligned} $$ | |
| ① | Multiply $15y^2$ by $ \dfrac{y+3}{10} $ to get $ \dfrac{ 15y^3+45y^2 }{ 10 } $. Step 1: Write $ 15y^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 15y^2 \cdot \frac{y+3}{10} & \xlongequal{\text{Step 1}} \frac{15y^2}{\color{red}{1}} \cdot \frac{y+3}{10} \xlongequal{\text{Step 2}} \frac{ 15y^2 \cdot \left( y+3 \right) }{ 1 \cdot 10 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15y^3+45y^2 }{ 10 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{15y^3+45y^2}{10} $ by $ y^3 $ to get $ \dfrac{ 15y^6+45y^5 }{ 10 } $. Step 1: Write $ y^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{15y^3+45y^2}{10} \cdot y^3 & \xlongequal{\text{Step 1}} \frac{15y^3+45y^2}{10} \cdot \frac{y^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 15y^3+45y^2 \right) \cdot y^3 }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15y^6+45y^5 }{ 10 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{15y^6+45y^5}{10} $ by $ y+3 $ to get $ \dfrac{15y^7+90y^6+135y^5}{10} $. Step 1: Write $ y+3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{15y^6+45y^5}{10} \cdot y+3 & \xlongequal{\text{Step 1}} \frac{15y^6+45y^5}{10} \cdot \frac{y+3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 15y^6+45y^5 \right) \cdot \left( y+3 \right) }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15y^7+45y^6+45y^6+135y^5 }{ 10 } = \frac{15y^7+90y^6+135y^5}{10} \end{aligned} $$ |