Question
Answer
$$1-(1+x)^3=-x^3-3x^2-3x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}1-(1+x)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}1-(1+3x+3x^2+x^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1-1-3x-3x^2-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{1} -\cancel{1}-3x-3x^2-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^3-3x^2-3x\end{aligned} $$ | |
| ① | Find $ \left(1+x\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 1 $ and $ B = x $. $$ \left(1+x\right)^3 = 1^3+3 \cdot 1^2 \cdot x + 3 \cdot 1 \cdot x^2+x^3 = 1+3x+3x^2+x^3 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 1+3x+3x^2+x^3 \right) = -1-3x-3x^2-x^3 $$ |
| ③ | Combine like terms: $$ \, \color{blue}{ \cancel{1}} \, \, \color{blue}{ -\cancel{1}} \,-3x-3x^2-x^3 = -x^3-3x^2-3x $$ |
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