$$24x^3y^2-18x\cdot\dfrac{y^2}{3}xy=\dfrac{72x^3y^2-18x^2y^3}{3}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}24x^3y^2-18x \cdot \frac{y^2}{3}xy& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}24x^3y^2-\frac{18xy^2}{3}xy \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}24x^3y^2-\frac{18x^2y^2}{3}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}24x^3y^2-\frac{18x^2y^3}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{72x^3y^2-18x^2y^3}{3}\end{aligned} $$ | |
| ① | Multiply $18x$ by $ \dfrac{y^2}{3} $ to get $ \dfrac{ 18xy^2 }{ 3 } $. Step 1: Write $ 18x $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 18x \cdot \frac{y^2}{3} & \xlongequal{\text{Step 1}} \frac{18x}{\color{red}{1}} \cdot \frac{y^2}{3} \xlongequal{\text{Step 2}} \frac{ 18x \cdot y^2 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18xy^2 }{ 3 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{18xy^2}{3} $ by $ x $ to get $ \dfrac{ 18x^2y^2 }{ 3 } $. 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. $$ \begin{aligned} \frac{18xy^2}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{18xy^2}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 18xy^2 \cdot x }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18x^2y^2 }{ 3 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{18x^2y^2}{3} $ by $ y $ to get $ \dfrac{ 18x^2y^3 }{ 3 } $. 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. $$ \begin{aligned} \frac{18x^2y^2}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{18x^2y^2}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 18x^2y^2 \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18x^2y^3 }{ 3 } \end{aligned} $$ |
| ④ | Subtract $ \dfrac{18x^2y^3}{3} $ from $ 24x^3y^2 $ to get $ \dfrac{ \color{purple}{ 72x^3y^2-18x^2y^3 } }{ 3 }$. Step 1: Write $ 24x^3y^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. |