Question
Answer
$$(x-2)(x+1)(x+10)+12(x+8)^2=x^3+21x^2+180x+748$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x+1)(x+10)+12(x+8)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x-2)(x+1)(x+10)+12(x^2+16x+64) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+x-2x-2)(x+10)+12x^2+192x+768 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^2-x-2)(x+10)+12x^2+192x+768 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+10x^2-x^2-10x-2x-20+12x^2+192x+768 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^3+9x^2-12x-20+12x^2+192x+768 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^3+21x^2+180x+748\end{aligned} $$ | |
| ① | Find $ \left(x+8\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}{ 8 }$. $$ \begin{aligned}\left(x+8\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 8 + \color{red}{8^2} = x^2+16x+64\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x+1\right) = x^2+x-2x-2 $$Multiply $ \color{blue}{12} $ by $ \left( x^2+16x+64\right) $ $$ \color{blue}{12} \cdot \left( x^2+16x+64\right) = 12x^2+192x+768 $$ |
| ③ | Combine like terms: $$ x^2+ \color{blue}{x} \color{blue}{-2x} -2 = x^2 \color{blue}{-x} -2 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^2-x-2}\right) $ by each term in $ \left( x+10\right) $. $$ \left( \color{blue}{x^2-x-2}\right) \cdot \left( x+10\right) = x^3+10x^2-x^2-10x-2x-20 $$ |
| ⑤ | Combine like terms: $$ x^3+ \color{blue}{10x^2} \color{blue}{-x^2} \color{red}{-10x} \color{red}{-2x} -20 = x^3+ \color{blue}{9x^2} \color{red}{-12x} -20 $$ |
| ⑥ | Combine like terms: $$ x^3+ \color{blue}{9x^2} \color{red}{-12x} \color{green}{-20} + \color{blue}{12x^2} + \color{red}{192x} + \color{green}{768} = x^3+ \color{blue}{21x^2} + \color{red}{180x} + \color{green}{748} $$ |
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