Question
Answer
$$-2(x+2)^3(x+1)^2(x+5)=-2x^6-26x^5-130x^4-326x^3-436x^2-296x-80$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-2(x+2)^3(x+1)^2(x+5)& \xlongequal{ }-2(x^3+6x^2+12x+8)(x^2+2x+1)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^3+12x^2+24x+16)(x^2+2x+1)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^5+16x^4+50x^3+76x^2+56x+16)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(2x^6+26x^5+130x^4+326x^3+436x^2+296x+80) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2x^6-26x^5-130x^4-326x^3-436x^2-296x-80\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x^5+16x^4+50x^3+76x^2+56x+16}\right) $ by each term in $ \left( x+5\right) $. $$ \left( \color{blue}{2x^5+16x^4+50x^3+76x^2+56x+16}\right) \cdot \left( x+5\right) = \\ = 2x^6+10x^5+16x^5+80x^4+50x^4+250x^3+76x^3+380x^2+56x^2+280x+16x+80 $$ |
| ② | Combine like terms: $$ 2x^6+ \color{blue}{10x^5} + \color{blue}{16x^5} + \color{red}{80x^4} + \color{red}{50x^4} + \color{green}{250x^3} + \color{green}{76x^3} + \color{orange}{380x^2} + \color{orange}{56x^2} + \color{blue}{280x} + \color{blue}{16x} +80 = \\ = 2x^6+ \color{blue}{26x^5} + \color{red}{130x^4} + \color{green}{326x^3} + \color{orange}{436x^2} + \color{blue}{296x} +80 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(2x^6+26x^5+130x^4+326x^3+436x^2+296x+80 \right) = -2x^6-26x^5-130x^4-326x^3-436x^2-296x-80 $$ |
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