$$2x\cdot\dfrac{5-x}{5}x^2(x-5)=\dfrac{-2x^5+20x^4-50x^3}{5}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2x \cdot \frac{5-x}{5}x^2(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-2x^2+10x}{5}x^2(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-2x^4+10x^3}{5}(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-2x^5+20x^4-50x^3}{5}\end{aligned} $$ | |
| ① | Multiply $2x$ by $ \dfrac{5-x}{5} $ to get $ \dfrac{-2x^2+10x}{5} $. Step 1: Write $ 2x $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 2x \cdot \frac{5-x}{5} & \xlongequal{\text{Step 1}} \frac{2x}{\color{red}{1}} \cdot \frac{5-x}{5} \xlongequal{\text{Step 2}} \frac{ 2x \cdot \left( 5-x \right) }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x-2x^2 }{ 5 } = \frac{-2x^2+10x}{5} \end{aligned} $$ |
| ② | Multiply $ \dfrac{-2x^2+10x}{5} $ by $ x^2 $ to get $ \dfrac{ -2x^4+10x^3 }{ 5 } $. Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{-2x^2+10x}{5} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{-2x^2+10x}{5} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -2x^2+10x \right) \cdot x^2 }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -2x^4+10x^3 }{ 5 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{-2x^4+10x^3}{5} $ by $ x-5 $ to get $ \dfrac{-2x^5+20x^4-50x^3}{5} $. Step 1: Write $ x-5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{-2x^4+10x^3}{5} \cdot x-5 & \xlongequal{\text{Step 1}} \frac{-2x^4+10x^3}{5} \cdot \frac{x-5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -2x^4+10x^3 \right) \cdot \left( x-5 \right) }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -2x^5+10x^4+10x^4-50x^3 }{ 5 } = \frac{-2x^5+20x^4-50x^3}{5} \end{aligned} $$ |