\left( x-y+ \frac{ 4xy }{ x-y } \right) \left( x+y- \frac{ 4xy }{ x+ { y }^{ } } \right)
Evaluate
x^{2}-y^{2}
Expand
x^{2}-y^{2}
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\left(\frac{\left(x-y\right)\left(x-y\right)}{x-y}+\frac{4xy}{x-y}\right)\left(x+y-\frac{4xy}{x+y^{1}}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x-y times \frac{x-y}{x-y}.
\frac{\left(x-y\right)\left(x-y\right)+4xy}{x-y}\left(x+y-\frac{4xy}{x+y^{1}}\right)
Since \frac{\left(x-y\right)\left(x-y\right)}{x-y} and \frac{4xy}{x-y} have the same denominator, add them by adding their numerators.
\frac{x^{2}-xy-xy+y^{2}+4xy}{x-y}\left(x+y-\frac{4xy}{x+y^{1}}\right)
Do the multiplications in \left(x-y\right)\left(x-y\right)+4xy.
\frac{x^{2}+y^{2}+2xy}{x-y}\left(x+y-\frac{4xy}{x+y^{1}}\right)
Combine like terms in x^{2}-xy-xy+y^{2}+4xy.
\frac{x^{2}+y^{2}+2xy}{x-y}\left(x+y-\frac{4xy}{x+y}\right)
Calculate y to the power of 1 and get y.
\frac{x^{2}+y^{2}+2xy}{x-y}\left(\frac{\left(x+y\right)\left(x+y\right)}{x+y}-\frac{4xy}{x+y}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x+y times \frac{x+y}{x+y}.
\frac{x^{2}+y^{2}+2xy}{x-y}\times \frac{\left(x+y\right)\left(x+y\right)-4xy}{x+y}
Since \frac{\left(x+y\right)\left(x+y\right)}{x+y} and \frac{4xy}{x+y} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+y^{2}+2xy}{x-y}\times \frac{x^{2}+xy+xy+y^{2}-4xy}{x+y}
Do the multiplications in \left(x+y\right)\left(x+y\right)-4xy.
\frac{x^{2}+y^{2}+2xy}{x-y}\times \frac{x^{2}+y^{2}-2xy}{x+y}
Combine like terms in x^{2}+xy+xy+y^{2}-4xy.
\frac{\left(x^{2}+y^{2}+2xy\right)\left(x^{2}+y^{2}-2xy\right)}{\left(x-y\right)\left(x+y\right)}
Multiply \frac{x^{2}+y^{2}+2xy}{x-y} times \frac{x^{2}+y^{2}-2xy}{x+y} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x+y\right)^{2}\left(x-y\right)^{2}}{\left(x+y\right)\left(x-y\right)}
Factor the expressions that are not already factored.
\left(x+y\right)\left(x-y\right)
Cancel out \left(x+y\right)\left(x-y\right) in both numerator and denominator.
x^{2}-y^{2}
Expand the expression.
\left(\frac{\left(x-y\right)\left(x-y\right)}{x-y}+\frac{4xy}{x-y}\right)\left(x+y-\frac{4xy}{x+y^{1}}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x-y times \frac{x-y}{x-y}.
\frac{\left(x-y\right)\left(x-y\right)+4xy}{x-y}\left(x+y-\frac{4xy}{x+y^{1}}\right)
Since \frac{\left(x-y\right)\left(x-y\right)}{x-y} and \frac{4xy}{x-y} have the same denominator, add them by adding their numerators.
\frac{x^{2}-xy-xy+y^{2}+4xy}{x-y}\left(x+y-\frac{4xy}{x+y^{1}}\right)
Do the multiplications in \left(x-y\right)\left(x-y\right)+4xy.
\frac{x^{2}+y^{2}+2xy}{x-y}\left(x+y-\frac{4xy}{x+y^{1}}\right)
Combine like terms in x^{2}-xy-xy+y^{2}+4xy.
\frac{x^{2}+y^{2}+2xy}{x-y}\left(x+y-\frac{4xy}{x+y}\right)
Calculate y to the power of 1 and get y.
\frac{x^{2}+y^{2}+2xy}{x-y}\left(\frac{\left(x+y\right)\left(x+y\right)}{x+y}-\frac{4xy}{x+y}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x+y times \frac{x+y}{x+y}.
\frac{x^{2}+y^{2}+2xy}{x-y}\times \frac{\left(x+y\right)\left(x+y\right)-4xy}{x+y}
Since \frac{\left(x+y\right)\left(x+y\right)}{x+y} and \frac{4xy}{x+y} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+y^{2}+2xy}{x-y}\times \frac{x^{2}+xy+xy+y^{2}-4xy}{x+y}
Do the multiplications in \left(x+y\right)\left(x+y\right)-4xy.
\frac{x^{2}+y^{2}+2xy}{x-y}\times \frac{x^{2}+y^{2}-2xy}{x+y}
Combine like terms in x^{2}+xy+xy+y^{2}-4xy.
\frac{\left(x^{2}+y^{2}+2xy\right)\left(x^{2}+y^{2}-2xy\right)}{\left(x-y\right)\left(x+y\right)}
Multiply \frac{x^{2}+y^{2}+2xy}{x-y} times \frac{x^{2}+y^{2}-2xy}{x+y} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x+y\right)^{2}\left(x-y\right)^{2}}{\left(x+y\right)\left(x-y\right)}
Factor the expressions that are not already factored.
\left(x+y\right)\left(x-y\right)
Cancel out \left(x+y\right)\left(x-y\right) in both numerator and denominator.
x^{2}-y^{2}
Expand the 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}