Factor
-\frac{\left(x-2\right)^{2}}{2}
Evaluate
-\frac{\left(x-2\right)^{2}}{2}
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\frac{-x^{2}+4x-4}{2}
Factor out \frac{1}{2}.
a+b=4 ab=-\left(-4\right)=4
Consider -x^{2}+4x-4. Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx-4. To find a and b, set up a system to be solved.
1,4 2,2
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 4.
1+4=5 2+2=4
Calculate the sum for each pair.
a=2 b=2
The solution is the pair that gives sum 4.
\left(-x^{2}+2x\right)+\left(2x-4\right)
Rewrite -x^{2}+4x-4 as \left(-x^{2}+2x\right)+\left(2x-4\right).
-x\left(x-2\right)+2\left(x-2\right)
Factor out -x in the first and 2 in the second group.
\left(x-2\right)\left(-x+2\right)
Factor out common term x-2 by using distributive property.
\frac{\left(x-2\right)\left(-x+2\right)}{2}
Rewrite the complete factored expression.
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}