Question
Answer
$$3x(1-x)^2=3x^3-6x^2+3x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3x(1-x)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3x(1-2x+x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x-6x^2+3x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^3-6x^2+3x\end{aligned} $$ | |
| ① | Find $ \left(1-x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 1 } $ and $ B = \color{red}{ x }$. $$ \begin{aligned}\left(1-x\right)^2 = \color{blue}{1^2} -2 \cdot 1 \cdot x + \color{red}{x^2} = 1-2x+x^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{3x} $ by $ \left( 1-2x+x^2\right) $ $$ \color{blue}{3x} \cdot \left( 1-2x+x^2\right) = 3x-6x^2+3x^3 $$ |
| ③ | Combine like terms: $$ 3x^3-6x^2+3x = 3x^3-6x^2+3x $$ |
This page was created using
Simplify polynomials calculator