Evaluate
x^{2}-4x+5
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x^{2}-4x+5
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\left(x-1\right)^{2}-\left(x-2\right)\times 2
Multiply x-1 and x-1 to get \left(x-1\right)^{2}.
x^{2}-2x+1-\left(x-2\right)\times 2
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
x^{2}-2x+1-\left(2x-4\right)
Use the distributive property to multiply x-2 by 2.
x^{2}-2x+1-2x-\left(-4\right)
To find the opposite of 2x-4, find the opposite of each term.
x^{2}-2x+1-2x+4
The opposite of -4 is 4.
x^{2}-4x+1+4
Combine -2x and -2x to get -4x.
x^{2}-4x+5
Add 1 and 4 to get 5.
\left(x-1\right)^{2}-\left(x-2\right)\times 2
Multiply x-1 and x-1 to get \left(x-1\right)^{2}.
x^{2}-2x+1-\left(x-2\right)\times 2
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
x^{2}-2x+1-\left(2x-4\right)
Use the distributive property to multiply x-2 by 2.
x^{2}-2x+1-2x-\left(-4\right)
To find the opposite of 2x-4, find the opposite of each term.
x^{2}-2x+1-2x+4
The opposite of -4 is 4.
x^{2}-4x+1+4
Combine -2x and -2x to get -4x.
x^{2}-4x+5
Add 1 and 4 to get 5.
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}