$$\dfrac{22}{3}(x-1)(x+3)(x+8)(x-6)(x+2)(x+5)(x+4)=\dfrac{22x^7+330x^6+770x^5-9394x^4-57288x^3-91784x^2+30624x+126720}{3}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{22}{3}(x-1)(x+3)(x+8)(x-6)(x+2)(x+5)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{22x-22}{3}(x+3)(x+8)(x-6)(x+2)(x+5)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{22x^2+44x-66}{3}(x+8)(x-6)(x+2)(x+5)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{22x^3+220x^2+286x-528}{3}(x-6)(x+2)(x+5)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{22x^4+88x^3-1034x^2-2244x+3168}{3}(x+2)(x+5)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{22x^5+132x^4-858x^3-4312x^2-1320x+6336}{3}(x+5)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{22x^6+242x^5-198x^4-8602x^3-22880x^2-264x+31680}{3}(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{22x^7+330x^6+770x^5-9394x^4-57288x^3-91784x^2+30624x+126720}{3}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{22}{3} $ by $ x-1 $ to get $ \dfrac{ 22x-22 }{ 3 } $. Step 1: Write $ x-1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{22}{3} \cdot x-1 & \xlongequal{\text{Step 1}} \frac{22}{3} \cdot \frac{x-1}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 22 \cdot \left( x-1 \right) }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 22x-22 }{ 3 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{22x-22}{3} $ by $ x+3 $ to get $ \dfrac{22x^2+44x-66}{3} $. Step 1: Write $ x+3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{22x-22}{3} \cdot x+3 & \xlongequal{\text{Step 1}} \frac{22x-22}{3} \cdot \frac{x+3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 22x-22 \right) \cdot \left( x+3 \right) }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 22x^2+66x-22x-66 }{ 3 } = \frac{22x^2+44x-66}{3} \end{aligned} $$ |
| ③ | Multiply $ \dfrac{22x^2+44x-66}{3} $ by $ x+8 $ to get $ \dfrac{22x^3+220x^2+286x-528}{3} $. 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. $$ \begin{aligned} \frac{22x^2+44x-66}{3} \cdot x+8 & \xlongequal{\text{Step 1}} \frac{22x^2+44x-66}{3} \cdot \frac{x+8}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 22x^2+44x-66 \right) \cdot \left( x+8 \right) }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 22x^3+176x^2+44x^2+352x-66x-528 }{ 3 } = \frac{22x^3+220x^2+286x-528}{3} \end{aligned} $$ |
| ④ | Multiply $ \dfrac{22x^3+220x^2+286x-528}{3} $ by $ x-6 $ to get $ \dfrac{22x^4+88x^3-1034x^2-2244x+3168}{3} $. 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. $$ \begin{aligned} \frac{22x^3+220x^2+286x-528}{3} \cdot x-6 & \xlongequal{\text{Step 1}} \frac{22x^3+220x^2+286x-528}{3} \cdot \frac{x-6}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 22x^3+220x^2+286x-528 \right) \cdot \left( x-6 \right) }{ 3 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 22x^4-132x^3+220x^3-1320x^2+286x^2-1716x-528x+3168 }{ 3 } = \\[1ex] &= \frac{22x^4+88x^3-1034x^2-2244x+3168}{3} \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{22x^4+88x^3-1034x^2-2244x+3168}{3} $ by $ x+2 $ to get $ \dfrac{22x^5+132x^4-858x^3-4312x^2-1320x+6336}{3} $. 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. $$ \begin{aligned} \frac{22x^4+88x^3-1034x^2-2244x+3168}{3} \cdot x+2 & \xlongequal{\text{Step 1}} \frac{22x^4+88x^3-1034x^2-2244x+3168}{3} \cdot \frac{x+2}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 22x^4+88x^3-1034x^2-2244x+3168 \right) \cdot \left( x+2 \right) }{ 3 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 22x^5+44x^4+88x^4+176x^3-1034x^3-2068x^2-2244x^2-4488x+3168x+6336 }{ 3 } = \\[1ex] &= \frac{22x^5+132x^4-858x^3-4312x^2-1320x+6336}{3} \end{aligned} $$ |
| ⑥ | Multiply $ \dfrac{22x^5+132x^4-858x^3-4312x^2-1320x+6336}{3} $ by $ x+5 $ to get $ \dfrac{22x^6+242x^5-198x^4-8602x^3-22880x^2-264x+31680}{3} $. 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. $$ \begin{aligned} \frac{22x^5+132x^4-858x^3-4312x^2-1320x+6336}{3} \cdot x+5 & \xlongequal{\text{Step 1}} \frac{22x^5+132x^4-858x^3-4312x^2-1320x+6336}{3} \cdot \frac{x+5}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 22x^5+132x^4-858x^3-4312x^2-1320x+6336 \right) \cdot \left( x+5 \right) }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 22x^6+110x^5+132x^5+660x^4-858x^4-4290x^3-4312x^3-21560x^2-1320x^2-6600x+6336x+31680 }{ 3 } = \frac{22x^6+242x^5-198x^4-8602x^3-22880x^2-264x+31680}{3} \end{aligned} $$ |
| ⑦ | Multiply $ \dfrac{22x^6+242x^5-198x^4-8602x^3-22880x^2-264x+31680}{3} $ by $ x+4 $ to get $ \dfrac{22x^7+330x^6+770x^5-9394x^4-57288x^3-91784x^2+30624x+126720}{3} $. Step 1: Write $ x+4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{22x^6+242x^5-198x^4-8602x^3-22880x^2-264x+31680}{3} \cdot x+4 & \xlongequal{\text{Step 1}} \frac{22x^6+242x^5-198x^4-8602x^3-22880x^2-264x+31680}{3} \cdot \frac{x+4}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 22x^6+242x^5-198x^4-8602x^3-22880x^2-264x+31680 \right) \cdot \left( x+4 \right) }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 22x^7+88x^6+242x^6+968x^5-198x^5-792x^4-8602x^4-34408x^3-22880x^3-91520x^2-264x^2-1056x+31680x+126720 }{ 3 } = \\[1ex] &= \frac{22x^7+330x^6+770x^5-9394x^4-57288x^3-91784x^2+30624x+126720}{3} \end{aligned} $$ |