Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4x^3\frac{y}{2}xy& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4x^3y}{2}xy \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4x^4y}{2}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4x^4y^2}{2}\end{aligned} $$ | |
| ① | Multiply $4x^3$ by $ \dfrac{y}{2} $ to get $ \dfrac{ 4x^3y }{ 2 } $. Step 1: Write $ 4x^3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 4x^3 \cdot \frac{y}{2} & \xlongequal{\text{Step 1}} \frac{4x^3}{\color{red}{1}} \cdot \frac{y}{2} \xlongequal{\text{Step 2}} \frac{ 4x^3 \cdot y }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^3y }{ 2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{4x^3y}{2} $ by $ x $ to get $ \dfrac{ 4x^4y }{ 2 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^3y}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{4x^3y}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^3y \cdot x }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4y }{ 2 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{4x^4y}{2} $ by $ y $ to get $ \dfrac{ 4x^4y^2 }{ 2 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^4y}{2} \cdot y & \xlongequal{\text{Step 1}} \frac{4x^4y}{2} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^4y \cdot y }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4y^2 }{ 2 } \end{aligned} $$ |