Evaluate
\left(2x-1\right)\left(x-2\right)^{2}
Expand
2x^{3}-9x^{2}+12x-4
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2x^{3}-x^{2}-4\left(2x-1\right)x+8x-4
Use the distributive property to multiply 2x-1 by x^{2}.
2x^{3}-x^{2}+\left(-8x+4\right)x+8x-4
Use the distributive property to multiply -4 by 2x-1.
2x^{3}-x^{2}-8x^{2}+4x+8x-4
Use the distributive property to multiply -8x+4 by x.
2x^{3}-9x^{2}+4x+8x-4
Combine -x^{2} and -8x^{2} to get -9x^{2}.
2x^{3}-9x^{2}+12x-4
Combine 4x and 8x to get 12x.
2x^{3}-x^{2}-4\left(2x-1\right)x+8x-4
Use the distributive property to multiply 2x-1 by x^{2}.
2x^{3}-x^{2}+\left(-8x+4\right)x+8x-4
Use the distributive property to multiply -4 by 2x-1.
2x^{3}-x^{2}-8x^{2}+4x+8x-4
Use the distributive property to multiply -8x+4 by x.
2x^{3}-9x^{2}+4x+8x-4
Combine -x^{2} and -8x^{2} to get -9x^{2}.
2x^{3}-9x^{2}+12x-4
Combine 4x and 8x to get 12x.
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}