Evaluate
\left(9-x\right)^{3}
Expand
729-243x+27x^{2}-x^{3}
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\left(-x\right)^{3}+27\left(-x\right)^{2}+243\left(-x\right)+729
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(-x+9\right)^{3}.
\left(-x\right)^{3}+27x^{2}+243\left(-x\right)+729
Calculate -x to the power of 2 and get x^{2}.
\left(-1\right)^{3}x^{3}+27x^{2}+243\left(-1\right)x+729
Expand \left(-x\right)^{3}.
-x^{3}+27x^{2}+243\left(-1\right)x+729
Calculate -1 to the power of 3 and get -1.
-x^{3}+27x^{2}-243x+729
Multiply 243 and -1 to get -243.
\left(-x\right)^{3}+27\left(-x\right)^{2}+243\left(-x\right)+729
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(-x+9\right)^{3}.
\left(-x\right)^{3}+27x^{2}+243\left(-x\right)+729
Calculate -x to the power of 2 and get x^{2}.
\left(-1\right)^{3}x^{3}+27x^{2}+243\left(-1\right)x+729
Expand \left(-x\right)^{3}.
-x^{3}+27x^{2}+243\left(-1\right)x+729
Calculate -1 to the power of 3 and get -1.
-x^{3}+27x^{2}-243x+729
Multiply 243 and -1 to get -243.
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}