Evaluate
2\left(x-2\right)\left(x^{2}-4x+7\right)
Expand
2x^{3}-12x^{2}+30x-28
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x^{3}-9x^{2}+27x-27+\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(x-3\right)^{3}.
x^{3}-9x^{2}+27x-27+x^{3}-3x^{2}+3x-1
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.
2x^{3}-9x^{2}+27x-27-3x^{2}+3x-1
Combine x^{3} and x^{3} to get 2x^{3}.
2x^{3}-12x^{2}+27x-27+3x-1
Combine -9x^{2} and -3x^{2} to get -12x^{2}.
2x^{3}-12x^{2}+30x-27-1
Combine 27x and 3x to get 30x.
2x^{3}-12x^{2}+30x-28
Subtract 1 from -27 to get -28.
x^{3}-9x^{2}+27x-27+\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(x-3\right)^{3}.
x^{3}-9x^{2}+27x-27+x^{3}-3x^{2}+3x-1
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.
2x^{3}-9x^{2}+27x-27-3x^{2}+3x-1
Combine x^{3} and x^{3} to get 2x^{3}.
2x^{3}-12x^{2}+27x-27+3x-1
Combine -9x^{2} and -3x^{2} to get -12x^{2}.
2x^{3}-12x^{2}+30x-27-1
Combine 27x and 3x to get 30x.
2x^{3}-12x^{2}+30x-28
Subtract 1 from -27 to get -28.
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}