Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-1)(x-2)(x-4)(x-7)(x-14)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-2x-x+2)(x-4)(x-7)(x-14) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-3x+2)(x-4)(x-7)(x-14) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-4x^2-3x^2+12x+2x-8)(x-7)(x-14) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3-7x^2+14x-8)(x-7)(x-14) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}(x^4-14x^3+63x^2-106x+56)(x-14) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}x^5-28x^4+259x^3-988x^2+1540x-784\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( x-2\right) = x^2-2x-x+2 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-2x} \color{blue}{-x} +2 = x^2 \color{blue}{-3x} +2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-3x+2}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^2-3x+2}\right) \cdot \left( x-4\right) = x^3-4x^2-3x^2+12x+2x-8 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-4x^2} \color{blue}{-3x^2} + \color{red}{12x} + \color{red}{2x} -8 = x^3 \color{blue}{-7x^2} + \color{red}{14x} -8 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3-7x^2+14x-8}\right) $ by each term in $ \left( x-7\right) $. $$ \left( \color{blue}{x^3-7x^2+14x-8}\right) \cdot \left( x-7\right) = x^4-7x^3-7x^3+49x^2+14x^2-98x-8x+56 $$ |
| ⑥ | Combine like terms: $$ x^4 \color{blue}{-7x^3} \color{blue}{-7x^3} + \color{red}{49x^2} + \color{red}{14x^2} \color{green}{-98x} \color{green}{-8x} +56 = \\ = x^4 \color{blue}{-14x^3} + \color{red}{63x^2} \color{green}{-106x} +56 $$ |
| ⑦ | Multiply each term of $ \left( \color{blue}{x^4-14x^3+63x^2-106x+56}\right) $ by each term in $ \left( x-14\right) $. $$ \left( \color{blue}{x^4-14x^3+63x^2-106x+56}\right) \cdot \left( x-14\right) = \\ = x^5-14x^4-14x^4+196x^3+63x^3-882x^2-106x^2+1484x+56x-784 $$ |
| ⑧ | Combine like terms: $$ x^5 \color{blue}{-14x^4} \color{blue}{-14x^4} + \color{red}{196x^3} + \color{red}{63x^3} \color{green}{-882x^2} \color{green}{-106x^2} + \color{orange}{1484x} + \color{orange}{56x} -784 = \\ = x^5 \color{blue}{-28x^4} + \color{red}{259x^3} \color{green}{-988x^2} + \color{orange}{1540x} -784 $$ |