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\frac{\left(x-y\right)^{2}}{2^{2}}-\left(\frac{x+y}{2}\right)^{2}
To raise \frac{x-y}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(x-y\right)^{2}}{2^{2}}-\frac{\left(x+y\right)^{2}}{2^{2}}
To raise \frac{x+y}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(x-y\right)^{2}}{2^{2}}-\frac{\left(x+y\right)^{2}}{4}
Calculate 2 to the power of 2 and get 4.
\frac{\left(x-y\right)^{2}}{4}-\frac{\left(x+y\right)^{2}}{4}
To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.
\frac{\left(x-y\right)^{2}-\left(x+y\right)^{2}}{4}
Since \frac{\left(x-y\right)^{2}}{4} and \frac{\left(x+y\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{4}
Do the multiplications in \left(x-y\right)^{2}-\left(x+y\right)^{2}.
\frac{-4xy}{4}
Combine like terms in x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}.
-xy
Cancel out 4 and 4.
\frac{\left(x-y\right)^{2}}{2^{2}}-\left(\frac{x+y}{2}\right)^{2}
To raise \frac{x-y}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(x-y\right)^{2}}{2^{2}}-\frac{\left(x+y\right)^{2}}{2^{2}}
To raise \frac{x+y}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(x-y\right)^{2}}{2^{2}}-\frac{\left(x+y\right)^{2}}{4}
Calculate 2 to the power of 2 and get 4.
\frac{\left(x-y\right)^{2}}{4}-\frac{\left(x+y\right)^{2}}{4}
To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.
\frac{\left(x-y\right)^{2}-\left(x+y\right)^{2}}{4}
Since \frac{\left(x-y\right)^{2}}{4} and \frac{\left(x+y\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{4}
Do the multiplications in \left(x-y\right)^{2}-\left(x+y\right)^{2}.
\frac{-4xy}{4}
Combine like terms in x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}.
-xy
Cancel out 4 and 4.
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}