Evaluate
\left(x-y\right)\left(5x-2y-1\right)
Expand
5x^{2}-7xy-x+2y^{2}+y
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3x^{2}-3xy+2\left(x^{2}-2xy+y^{2}\right)-x+y
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.
3x^{2}-3xy+2x^{2}-4xy+2y^{2}-x+y
Use the distributive property to multiply 2 by x^{2}-2xy+y^{2}.
5x^{2}-3xy-4xy+2y^{2}-x+y
Combine 3x^{2} and 2x^{2} to get 5x^{2}.
5x^{2}-7xy+2y^{2}-x+y
Combine -3xy and -4xy to get -7xy.
3x^{2}-3xy+2\left(x^{2}-2xy+y^{2}\right)-x+y
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.
3x^{2}-3xy+2x^{2}-4xy+2y^{2}-x+y
Use the distributive property to multiply 2 by x^{2}-2xy+y^{2}.
5x^{2}-3xy-4xy+2y^{2}-x+y
Combine 3x^{2} and 2x^{2} to get 5x^{2}.
5x^{2}-7xy+2y^{2}-x+y
Combine -3xy and -4xy to get -7xy.
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}