Tap the blue circles to see an explanation.
$$ \begin{aligned}(x+17)(x+2)^2(x-7)(x-9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x+17)(x^2+4x+4)(x-7)(x-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^3+4x^2+4x+17x^2+68x+68)(x-7)(x-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+21x^2+72x+68)(x-7)(x-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(x^4+14x^3-75x^2-436x-476)(x-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}x^5+5x^4-201x^3+239x^2+3448x+4284\end{aligned} $$ | |
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+17}\right) $ by each term in $ \left( x^2+4x+4\right) $. $$ \left( \color{blue}{x+17}\right) \cdot \left( x^2+4x+4\right) = x^3+4x^2+4x+17x^2+68x+68 $$ |
③ | Combine like terms: $$ x^3+ \color{blue}{4x^2} + \color{red}{4x} + \color{blue}{17x^2} + \color{red}{68x} +68 = x^3+ \color{blue}{21x^2} + \color{red}{72x} +68 $$ |
④ | Multiply each term of $ \left( \color{blue}{x^3+21x^2+72x+68}\right) $ by each term in $ \left( x-7\right) $. $$ \left( \color{blue}{x^3+21x^2+72x+68}\right) \cdot \left( x-7\right) = x^4-7x^3+21x^3-147x^2+72x^2-504x+68x-476 $$ |
⑤ | Combine like terms: $$ x^4 \color{blue}{-7x^3} + \color{blue}{21x^3} \color{red}{-147x^2} + \color{red}{72x^2} \color{green}{-504x} + \color{green}{68x} -476 = \\ = x^4+ \color{blue}{14x^3} \color{red}{-75x^2} \color{green}{-436x} -476 $$ |
⑥ | Multiply each term of $ \left( \color{blue}{x^4+14x^3-75x^2-436x-476}\right) $ by each term in $ \left( x-9\right) $. $$ \left( \color{blue}{x^4+14x^3-75x^2-436x-476}\right) \cdot \left( x-9\right) = \\ = x^5-9x^4+14x^4-126x^3-75x^3+675x^2-436x^2+3924x-476x+4284 $$ |
⑦ | Combine like terms: $$ x^5 \color{blue}{-9x^4} + \color{blue}{14x^4} \color{red}{-126x^3} \color{red}{-75x^3} + \color{green}{675x^2} \color{green}{-436x^2} + \color{orange}{3924x} \color{orange}{-476x} +4284 = \\ = x^5+ \color{blue}{5x^4} \color{red}{-201x^3} + \color{green}{239x^2} + \color{orange}{3448x} +4284 $$ |