$$10\cdot\dfrac{x}{5}y\cdot3xy-x^2y^2=\dfrac{25x^2y^2}{5}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10 \cdot \frac{x}{5}y\cdot3xy-x^2y^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10x}{5}y\cdot3xy-x^2y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10xy}{5}\cdot3xy-x^2y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{30xy}{5}xy-x^2y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{30x^2y}{5}y-x^2y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{30x^2y^2}{5}-x^2y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{25x^2y^2}{5}\end{aligned} $$ | |
| ① | Multiply $10$ by $ \dfrac{x}{5} $ to get $ \dfrac{ 10x }{ 5 } $. Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 10 \cdot \frac{x}{5} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{x}{5} \xlongequal{\text{Step 2}} \frac{ 10 \cdot x }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x }{ 5 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{10x}{5} $ by $ y $ to get $ \dfrac{ 10xy }{ 5 } $. 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. $$ \begin{aligned} \frac{10x}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{10x}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 10x \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10xy }{ 5 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{10xy}{5} $ by $ 3 $ to get $ \dfrac{ 30xy }{ 5 } $. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{10xy}{5} \cdot 3 & \xlongequal{\text{Step 1}} \frac{10xy}{5} \cdot \frac{3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 10xy \cdot 3 }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30xy }{ 5 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{30xy}{5} $ by $ x $ to get $ \dfrac{ 30x^2y }{ 5 } $. 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. $$ \begin{aligned} \frac{30xy}{5} \cdot x & \xlongequal{\text{Step 1}} \frac{30xy}{5} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 30xy \cdot x }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x^2y }{ 5 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{30x^2y}{5} $ by $ y $ to get $ \dfrac{ 30x^2y^2 }{ 5 } $. 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. $$ \begin{aligned} \frac{30x^2y}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{30x^2y}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 30x^2y \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x^2y^2 }{ 5 } \end{aligned} $$ |
| ⑥ | Subtract $x^2y^2$ from $ \dfrac{30x^2y^2}{5} $ to get $ \dfrac{ \color{purple}{ 25x^2y^2 } }{ 5 }$. Step 1: Write $ x^2y^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |