$$\dfrac{2}{100}(x-2)(x+7)(x-5)(x+8)=\dfrac{x^4+8x^3-39x^2-242x+560}{50}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{100}(x-2)(x+7)(x-5)(x+8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\left(\left(\left(\frac{ 2 : \color{orangered}{ 2 } }{ 100 : \color{orangered}{ 2 }} \cdot \left(x-2\right)\right) \cdot \left(x+7\right)\right) \cdot \left(x-5\right)\right) \cdot \left(x+8\right) \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{50}(x-2)(x+7)(x-5)(x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{x-2}{50}(x+7)(x-5)(x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{x^2+5x-14}{50}(x-5)(x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{x^3-39x+70}{50}(x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{x^4+8x^3-39x^2-242x+560}{50}\end{aligned} $$ | |
| ① | Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $. |
| ② | Multiply $ \dfrac{1}{50} $ by $ x-2 $ to get $ \dfrac{ x-2 }{ 50 } $. 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. $$ \begin{aligned} \frac{1}{50} \cdot x-2 & \xlongequal{\text{Step 1}} \frac{1}{50} \cdot \frac{x-2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x-2 \right) }{ 50 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x-2 }{ 50 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{x-2}{50} $ by $ x+7 $ to get $ \dfrac{x^2+5x-14}{50} $. Step 1: Write $ x+7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{x-2}{50} \cdot x+7 & \xlongequal{\text{Step 1}} \frac{x-2}{50} \cdot \frac{x+7}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x-2 \right) \cdot \left( x+7 \right) }{ 50 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2+7x-2x-14 }{ 50 } = \frac{x^2+5x-14}{50} \end{aligned} $$ |
| ④ | Multiply $ \dfrac{x^2+5x-14}{50} $ by $ x-5 $ to get $ \dfrac{x^3-39x+70}{50} $. 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. $$ \begin{aligned} \frac{x^2+5x-14}{50} \cdot x-5 & \xlongequal{\text{Step 1}} \frac{x^2+5x-14}{50} \cdot \frac{x-5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x^2+5x-14 \right) \cdot \left( x-5 \right) }{ 50 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^3 -\cancel{5x^2}+ \cancel{5x^2}-25x-14x+70 }{ 50 } = \frac{x^3-39x+70}{50} \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{x^3-39x+70}{50} $ by $ x+8 $ to get $ \dfrac{x^4+8x^3-39x^2-242x+560}{50} $. Step 1: Write $ x+8 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{x^3-39x+70}{50} \cdot x+8 & \xlongequal{\text{Step 1}} \frac{x^3-39x+70}{50} \cdot \frac{x+8}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x^3-39x+70 \right) \cdot \left( x+8 \right) }{ 50 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^4+8x^3-39x^2-312x+70x+560 }{ 50 } = \frac{x^4+8x^3-39x^2-242x+560}{50} \end{aligned} $$ |