$$16^4 \cdot \dfrac{y+8}{12}y^3(y+8)=\dfrac{65536y^5+1048576y^4+4194304y^3}{12}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}16^4\frac{y+8}{12}y^3(y+8)& \xlongequal{ }65536 \cdot \frac{y+8}{12}y^3(y+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{65536y+524288}{12}y^3(y+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{65536y^4+524288y^3}{12}(y+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{65536y^5+1048576y^4+4194304y^3}{12}\end{aligned} $$ | |
| ① | Multiply $65536$ by $ \dfrac{y+8}{12} $ to get $ \dfrac{ 65536y+524288 }{ 12 } $. Step 1: Write $ 65536 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 65536 \cdot \frac{y+8}{12} & \xlongequal{\text{Step 1}} \frac{65536}{\color{red}{1}} \cdot \frac{y+8}{12} \xlongequal{\text{Step 2}} \frac{ 65536 \cdot \left( y+8 \right) }{ 1 \cdot 12 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 65536y+524288 }{ 12 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{65536y+524288}{12} $ by $ y^3 $ to get $ \dfrac{ 65536y^4+524288y^3 }{ 12 } $. 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. $$ \begin{aligned} \frac{65536y+524288}{12} \cdot y^3 & \xlongequal{\text{Step 1}} \frac{65536y+524288}{12} \cdot \frac{y^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 65536y+524288 \right) \cdot y^3 }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 65536y^4+524288y^3 }{ 12 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{65536y^4+524288y^3}{12} $ by $ y+8 $ to get $ \dfrac{65536y^5+1048576y^4+4194304y^3}{12} $. Step 1: Write $ y+8 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{65536y^4+524288y^3}{12} \cdot y+8 & \xlongequal{\text{Step 1}} \frac{65536y^4+524288y^3}{12} \cdot \frac{y+8}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 65536y^4+524288y^3 \right) \cdot \left( y+8 \right) }{ 12 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 65536y^5+524288y^4+524288y^4+4194304y^3 }{ 12 } = \\[1ex] &= \frac{65536y^5+1048576y^4+4194304y^3}{12} \end{aligned} $$ |