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6x^{2}+2
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1-3x+3x^{2}-x^{3}-\left(-x-1\right)^{3}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(1-x\right)^{3}.
1-3x+3x^{2}-x^{3}-\left(\left(-x\right)^{3}-3\left(-x\right)^{2}+3\left(-x\right)-1\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(-x-1\right)^{3}.
1-3x+3x^{2}-x^{3}-\left(\left(-x\right)^{3}-3x^{2}+3\left(-x\right)-1\right)
Calculate -x to the power of 2 and get x^{2}.
1-3x+3x^{2}-x^{3}-\left(-x\right)^{3}+3x^{2}-3\left(-x\right)+1
To find the opposite of \left(-x\right)^{3}-3x^{2}+3\left(-x\right)-1, find the opposite of each term.
1-3x+6x^{2}-x^{3}-\left(-x\right)^{3}-3\left(-x\right)+1
Combine 3x^{2} and 3x^{2} to get 6x^{2}.
1-3x+6x^{2}-x^{3}-\left(-x\right)^{3}+3x+1
Multiply -3 and -1 to get 3.
1+6x^{2}-x^{3}-\left(-x\right)^{3}+1
Combine -3x and 3x to get 0.
2+6x^{2}-x^{3}-\left(-x\right)^{3}
Add 1 and 1 to get 2.
2+6x^{2}-x^{3}-\left(-1\right)^{3}x^{3}
Expand \left(-x\right)^{3}.
2+6x^{2}-x^{3}-\left(-x^{3}\right)
Calculate -1 to the power of 3 and get -1.
2+6x^{2}-x^{3}+x^{3}
Multiply -1 and -1 to get 1.
2+6x^{2}
Combine -x^{3} and x^{3} to get 0.
1-3x+3x^{2}-x^{3}-\left(-x-1\right)^{3}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(1-x\right)^{3}.
1-3x+3x^{2}-x^{3}-\left(\left(-x\right)^{3}-3\left(-x\right)^{2}+3\left(-x\right)-1\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(-x-1\right)^{3}.
1-3x+3x^{2}-x^{3}-\left(\left(-x\right)^{3}-3x^{2}+3\left(-x\right)-1\right)
Calculate -x to the power of 2 and get x^{2}.
1-3x+3x^{2}-x^{3}-\left(-x\right)^{3}+3x^{2}-3\left(-x\right)+1
To find the opposite of \left(-x\right)^{3}-3x^{2}+3\left(-x\right)-1, find the opposite of each term.
1-3x+6x^{2}-x^{3}-\left(-x\right)^{3}-3\left(-x\right)+1
Combine 3x^{2} and 3x^{2} to get 6x^{2}.
1-3x+6x^{2}-x^{3}-\left(-x\right)^{3}+3x+1
Multiply -3 and -1 to get 3.
1+6x^{2}-x^{3}-\left(-x\right)^{3}+1
Combine -3x and 3x to get 0.
2+6x^{2}-x^{3}-\left(-x\right)^{3}
Add 1 and 1 to get 2.
2+6x^{2}-x^{3}-\left(-1\right)^{3}x^{3}
Expand \left(-x\right)^{3}.
2+6x^{2}-x^{3}-\left(-x^{3}\right)
Calculate -1 to the power of 3 and get -1.
2+6x^{2}-x^{3}+x^{3}
Multiply -1 and -1 to get 1.
2+6x^{2}
Combine -x^{3} and x^{3} to get 0.
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}