Question
Answer
$$x^2(0.5-x)^3=-x^5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^2(0.5-x)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2(0+0x+0x^2-x^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}0x^2+0x^3+0x^4-x^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^5\end{aligned} $$ | |
| ① | Find $ \left(0-x\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 0 $ and $ B = x $. $$ \left(0-x\right)^3 = 0^3-3 \cdot 0^2 \cdot x + 3 \cdot 0 \cdot x^2-x^3 = 00x0x^2-x^3 $$ |
| ② | Multiply $ \color{blue}{x^2} $ by $ \left( 00x0x^2-x^3\right) $ $$ \color{blue}{x^2} \cdot \left( 00x0x^2-x^3\right) = 0x^20x^30x^4-x^5 $$ |
| ③ | Combine like terms: $$ -x^5 = -x^5 $$ |
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