Question
Answer
$$2(x+2)^2(x-3)(x+1)=2x^4+4x^3-14x^2-40x-24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x+2)^2(x-3)(x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2+4x+4)(x-3)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2+8x+8)(x-3)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(2x^3-6x^2+8x^2-24x+8x-24)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(2x^3+2x^2-16x-24)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}2x^4+4x^3-14x^2-40x-24\end{aligned} $$ | |
| 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 $ \color{blue}{2} $ by $ \left( x^2+4x+4\right) $ $$ \color{blue}{2} \cdot \left( x^2+4x+4\right) = 2x^2+8x+8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2+8x+8}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{2x^2+8x+8}\right) \cdot \left( x-3\right) = 2x^3-6x^2+8x^2-24x+8x-24 $$ |
| ④ | Combine like terms: $$ 2x^3 \color{blue}{-6x^2} + \color{blue}{8x^2} \color{red}{-24x} + \color{red}{8x} -24 = 2x^3+ \color{blue}{2x^2} \color{red}{-16x} -24 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{2x^3+2x^2-16x-24}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{2x^3+2x^2-16x-24}\right) \cdot \left( x+1\right) = 2x^4+2x^3+2x^3+2x^2-16x^2-16x-24x-24 $$ |
| ⑥ | Combine like terms: $$ 2x^4+ \color{blue}{2x^3} + \color{blue}{2x^3} + \color{red}{2x^2} \color{red}{-16x^2} \color{green}{-16x} \color{green}{-24x} -24 = 2x^4+ \color{blue}{4x^3} \color{red}{-14x^2} \color{green}{-40x} -24 $$ |
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