Question
Answer
$$-5x(x+1)^4=-5x^5-20x^4-30x^3-20x^2-5x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-5x(x+1)^4& \xlongequal{ }-5x(x^4+4x^3+6x^2+4x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(5x^5+20x^4+30x^3+20x^2+5x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-5x^5-20x^4-30x^3-20x^2-5x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{5x} $ by $ \left( x^4+4x^3+6x^2+4x+1\right) $ $$ \color{blue}{5x} \cdot \left( x^4+4x^3+6x^2+4x+1\right) = 5x^5+20x^4+30x^3+20x^2+5x $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(5x^5+20x^4+30x^3+20x^2+5x \right) = -5x^5-20x^4-30x^3-20x^2-5x $$ |
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