$$36(x-7)\dfrac{3x-2}{6}(3x-2)(x+6)=\dfrac{324x^4-756x^3-13032x^2+18000x-6048}{6}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}36(x-7)\frac{3x-2}{6}(3x-2)(x+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(36x-252)\frac{3x-2}{6}(3x-2)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{108x^2-828x+504}{6}(3x-2)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{324x^3-2700x^2+3168x-1008}{6}(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{324x^4-756x^3-13032x^2+18000x-6048}{6}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{36} $ by $ \left( x-7\right) $ $$ \color{blue}{36} \cdot \left( x-7\right) = 36x-252 $$ |
| ② | Multiply $36x-252$ by $ \dfrac{3x-2}{6} $ to get $ \dfrac{108x^2-828x+504}{6} $. Step 1: Write $ 36x-252 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 36x-252 \cdot \frac{3x-2}{6} & \xlongequal{\text{Step 1}} \frac{36x-252}{\color{red}{1}} \cdot \frac{3x-2}{6} \xlongequal{\text{Step 2}} \frac{ \left( 36x-252 \right) \cdot \left( 3x-2 \right) }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 108x^2-72x-756x+504 }{ 6 } = \frac{108x^2-828x+504}{6} \end{aligned} $$ |
| ③ | Multiply $ \dfrac{108x^2-828x+504}{6} $ by $ 3x-2 $ to get $ \dfrac{324x^3-2700x^2+3168x-1008}{6} $. Step 1: Write $ 3x-2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{108x^2-828x+504}{6} \cdot 3x-2 & \xlongequal{\text{Step 1}} \frac{108x^2-828x+504}{6} \cdot \frac{3x-2}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 108x^2-828x+504 \right) \cdot \left( 3x-2 \right) }{ 6 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 324x^3-216x^2-2484x^2+1656x+1512x-1008 }{ 6 } = \\[1ex] &= \frac{324x^3-2700x^2+3168x-1008}{6} \end{aligned} $$ |
| ④ | Multiply $ \dfrac{324x^3-2700x^2+3168x-1008}{6} $ by $ x+6 $ to get $ \dfrac{324x^4-756x^3-13032x^2+18000x-6048}{6} $. Step 1: Write $ x+6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{324x^3-2700x^2+3168x-1008}{6} \cdot x+6 & \xlongequal{\text{Step 1}} \frac{324x^3-2700x^2+3168x-1008}{6} \cdot \frac{x+6}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 324x^3-2700x^2+3168x-1008 \right) \cdot \left( x+6 \right) }{ 6 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 324x^4+1944x^3-2700x^3-16200x^2+3168x^2+19008x-1008x-6048 }{ 6 } = \\[1ex] &= \frac{324x^4-756x^3-13032x^2+18000x-6048}{6} \end{aligned} $$ |