Evaluate
\left(1-x\right)x^{2}\left(\left(1-x\right)^{2}+x\right)
Expand
x^{2}-2x^{3}+2x^{4}-x^{5}
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x^{2}\left(1-x\right)\left(1-2x+x^{2}+x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x\right)^{2}.
x^{2}\left(1-x\right)\left(1-x+x^{2}\right)
Combine -2x and x to get -x.
\left(x^{2}-x^{3}\right)\left(1-x+x^{2}\right)
Use the distributive property to multiply x^{2} by 1-x.
x^{2}-2x^{3}+2x^{4}-x^{5}
Use the distributive property to multiply x^{2}-x^{3} by 1-x+x^{2} and combine like terms.
x^{2}\left(1-x\right)\left(1-2x+x^{2}+x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x\right)^{2}.
x^{2}\left(1-x\right)\left(1-x+x^{2}\right)
Combine -2x and x to get -x.
\left(x^{2}-x^{3}\right)\left(1-x+x^{2}\right)
Use the distributive property to multiply x^{2} by 1-x.
x^{2}-2x^{3}+2x^{4}-x^{5}
Use the distributive property to multiply x^{2}-x^{3} by 1-x+x^{2} and combine like terms.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}