Evaluate
x^{2}+2xy+3y-2
Expand
x^{2}+2xy+3y-2
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x^{2}+2x+1+2\left(x+1\right)\left(y-1\right)+y-1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+1+\left(2x+2\right)\left(y-1\right)+y-1
Use the distributive property to multiply 2 by x+1.
x^{2}+2x+1+2xy-2x+2y-2+y-1
Use the distributive property to multiply 2x+2 by y-1.
x^{2}+1+2xy+2y-2+y-1
Combine 2x and -2x to get 0.
x^{2}-1+2xy+2y+y-1
Subtract 2 from 1 to get -1.
x^{2}-1+2xy+3y-1
Combine 2y and y to get 3y.
x^{2}-2+2xy+3y
Subtract 1 from -1 to get -2.
x^{2}+2x+1+2\left(x+1\right)\left(y-1\right)+y-1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+1+\left(2x+2\right)\left(y-1\right)+y-1
Use the distributive property to multiply 2 by x+1.
x^{2}+2x+1+2xy-2x+2y-2+y-1
Use the distributive property to multiply 2x+2 by y-1.
x^{2}+1+2xy+2y-2+y-1
Combine 2x and -2x to get 0.
x^{2}-1+2xy+2y+y-1
Subtract 2 from 1 to get -1.
x^{2}-1+2xy+3y-1
Combine 2y and y to get 3y.
x^{2}-2+2xy+3y
Subtract 1 from -1 to get -2.
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}