Question
Answer
$$-4x^2(x+1)^3=-4x^5-12x^4-12x^3-4x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-4x^2(x+1)^3& \xlongequal{ }-4x^2(x^3+3x^2+3x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(4x^5+12x^4+12x^3+4x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4x^5-12x^4-12x^3-4x^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4x^2} $ by $ \left( x^3+3x^2+3x+1\right) $ $$ \color{blue}{4x^2} \cdot \left( x^3+3x^2+3x+1\right) = 4x^5+12x^4+12x^3+4x^2 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(4x^5+12x^4+12x^3+4x^2 \right) = -4x^5-12x^4-12x^3-4x^2 $$ |
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