Answer
$$3\cdot\frac{x}{5}\cdot(5-25x)=\frac{-75x^2+15x}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3 \cdot \frac{x}{5}\cdot(5-25x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3x}{5}\cdot(5-25x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-75x^2+15x}{5}\end{aligned} $$ | |
| ① | Multiply $3$ by $ \dfrac{x}{5} $ to get $ \dfrac{ 3x }{ 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. $$ \begin{aligned} 3 \cdot \frac{x}{5} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{x}{5} \xlongequal{\text{Step 2}} \frac{ 3 \cdot x }{ 1 \cdot 5 } \xlongequal{\text{Step 3}} \frac{ 3x }{ 5 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{3x}{5} $ by $ 5-25x $ to get $ \dfrac{-75x^2+15x}{5} $. Step 1: Write $ 5-25x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3x}{5} \cdot 5-25x & \xlongequal{\text{Step 1}} \frac{3x}{5} \cdot \frac{5-25x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3x \cdot \left( 5-25x \right) }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15x-75x^2 }{ 5 } = \frac{-75x^2+15x}{5} \end{aligned} $$ |
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