Evaluate
\left(x-y\right)\left(x+3y\right)
Expand
x^{2}+2xy-3y^{2}
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\left(2x-2y\right)\left(x+y\right)-\left(x-y\right)^{2}
Use the distributive property to multiply 2 by x-y.
2x^{2}-2y^{2}-\left(x-y\right)^{2}
Use the distributive property to multiply 2x-2y by x+y and combine like terms.
2x^{2}-2y^{2}-\left(x^{2}-2xy+y^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.
2x^{2}-2y^{2}-x^{2}+2xy-y^{2}
To find the opposite of x^{2}-2xy+y^{2}, find the opposite of each term.
x^{2}-2y^{2}+2xy-y^{2}
Combine 2x^{2} and -x^{2} to get x^{2}.
x^{2}-3y^{2}+2xy
Combine -2y^{2} and -y^{2} to get -3y^{2}.
\left(2x-2y\right)\left(x+y\right)-\left(x-y\right)^{2}
Use the distributive property to multiply 2 by x-y.
2x^{2}-2y^{2}-\left(x-y\right)^{2}
Use the distributive property to multiply 2x-2y by x+y and combine like terms.
2x^{2}-2y^{2}-\left(x^{2}-2xy+y^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.
2x^{2}-2y^{2}-x^{2}+2xy-y^{2}
To find the opposite of x^{2}-2xy+y^{2}, find the opposite of each term.
x^{2}-2y^{2}+2xy-y^{2}
Combine 2x^{2} and -x^{2} to get x^{2}.
x^{2}-3y^{2}+2xy
Combine -2y^{2} and -y^{2} to get -3y^{2}.
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
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Matrix
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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}