Question
Answer
$$2(x-5)(x+1)^2=2x^3-6x^2-18x-10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-5)(x+1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x-5)(x^2+2x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x-10)(x^2+2x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+4x^2+2x-10x^2-20x-10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3-6x^2-18x-10\end{aligned} $$ | |
| ① | Find $ \left(x+1\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}{ 1 }$. $$ \begin{aligned}\left(x+1\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 1 + \color{red}{1^2} = x^2+2x+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x-5\right) $ $$ \color{blue}{2} \cdot \left( x-5\right) = 2x-10 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x-10}\right) $ by each term in $ \left( x^2+2x+1\right) $. $$ \left( \color{blue}{2x-10}\right) \cdot \left( x^2+2x+1\right) = 2x^3+4x^2+2x-10x^2-20x-10 $$ |
| ④ | Combine like terms: $$ 2x^3+ \color{blue}{4x^2} + \color{red}{2x} \color{blue}{-10x^2} \color{red}{-20x} -10 = 2x^3 \color{blue}{-6x^2} \color{red}{-18x} -10 $$ |
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