Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)^2(x-0)(x-4)(x-8)(x-13)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+4x+4)(x-0)(x-4)(x-8)(x-13) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^3+0x^2+4x^2+0x+4x+0)(x-4)(x-8)(x-13) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+4x^2+4x)(x-4)(x-8)(x-13) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^4-4x^3+4x^3-16x^2+4x^2-16x)(x-8)(x-13) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(x^4-12x^2-16x)(x-8)(x-13) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}(x^5-8x^4-12x^3+96x^2-16x^2+128x)(x-13) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}(x^5-8x^4-12x^3+80x^2+128x)(x-13) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}x^6-21x^5+92x^4+236x^3-912x^2-1664x\end{aligned} $$ | |
| ① | Find $ \left(x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(x+2\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2 + \color{red}{2^2} = x^2+4x+4\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2+4x+4}\right) $ by each term in $ \left( x0\right) $. $$ \left( \color{blue}{x^2+4x+4}\right) \cdot \left( x0\right) = x^30x^2+4x^20x+4x0 $$ |
| ③ | Combine like terms: $$ x^3 \color{blue}{0x^2} + \color{blue}{4x^2} \color{red}{0x} + \color{red}{4x} 0 = x^3+ \color{blue}{4x^2} + \color{red}{4x} $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^3+4x^2+4x}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^3+4x^2+4x}\right) \cdot \left( x-4\right) = x^4 -\cancel{4x^3}+ \cancel{4x^3}-16x^2+4x^2-16x $$ |
| ⑤ | Combine like terms: $$ x^4 \, \color{blue}{ -\cancel{4x^3}} \,+ \, \color{blue}{ \cancel{4x^3}} \, \color{green}{-16x^2} + \color{green}{4x^2} -16x = x^4 \color{green}{-12x^2} -16x $$ |
| ⑥ | Multiply each term of $ \left( \color{blue}{x^4-12x^2-16x}\right) $ by each term in $ \left( x-8\right) $. $$ \left( \color{blue}{x^4-12x^2-16x}\right) \cdot \left( x-8\right) = x^5-8x^4-12x^3+96x^2-16x^2+128x $$ |
| ⑦ | Combine like terms: $$ x^5-8x^4-12x^3+ \color{blue}{96x^2} \color{blue}{-16x^2} +128x = x^5-8x^4-12x^3+ \color{blue}{80x^2} +128x $$ |
| ⑧ | Multiply each term of $ \left( \color{blue}{x^5-8x^4-12x^3+80x^2+128x}\right) $ by each term in $ \left( x-13\right) $. $$ \left( \color{blue}{x^5-8x^4-12x^3+80x^2+128x}\right) \cdot \left( x-13\right) = \\ = x^6-13x^5-8x^5+104x^4-12x^4+156x^3+80x^3-1040x^2+128x^2-1664x $$ |
| ⑨ | Combine like terms: $$ x^6 \color{blue}{-13x^5} \color{blue}{-8x^5} + \color{red}{104x^4} \color{red}{-12x^4} + \color{green}{156x^3} + \color{green}{80x^3} \color{orange}{-1040x^2} + \color{orange}{128x^2} -1664x = \\ = x^6 \color{blue}{-21x^5} + \color{red}{92x^4} + \color{green}{236x^3} \color{orange}{-912x^2} -1664x $$ |