Evaluate
2\left(2-x\right)^{2}-\frac{1}{3}
Expand
2x^{2}-8x+\frac{23}{3}
Graph
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\left(\left(-x\right)^{2}+4\left(-x\right)+4\right)\times 2-\frac{1}{3}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-x+2\right)^{2}.
\left(x^{2}+4\left(-x\right)+4\right)\times 2-\frac{1}{3}
Calculate -x to the power of 2 and get x^{2}.
2x^{2}+8\left(-x\right)+8-\frac{1}{3}
Use the distributive property to multiply x^{2}+4\left(-x\right)+4 by 2.
2x^{2}+8\left(-x\right)+\frac{23}{3}
Subtract \frac{1}{3} from 8 to get \frac{23}{3}.
2x^{2}-8x+\frac{23}{3}
Multiply 8 and -1 to get -8.
\left(\left(-x\right)^{2}+4\left(-x\right)+4\right)\times 2-\frac{1}{3}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-x+2\right)^{2}.
\left(x^{2}+4\left(-x\right)+4\right)\times 2-\frac{1}{3}
Calculate -x to the power of 2 and get x^{2}.
2x^{2}+8\left(-x\right)+8-\frac{1}{3}
Use the distributive property to multiply x^{2}+4\left(-x\right)+4 by 2.
2x^{2}+8\left(-x\right)+\frac{23}{3}
Subtract \frac{1}{3} from 8 to get \frac{23}{3}.
2x^{2}-8x+\frac{23}{3}
Multiply 8 and -1 to get -8.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}