Evaluate
8y+y^{2}+4x-12xy
Expand
8y+y^{2}+4x-12xy
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4x^{2}-4xy+y^{2}-4\left(x-1\right)\left(x+2y\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.
4x^{2}-4xy+y^{2}+\left(-4x+4\right)\left(x+2y\right)
Use the distributive property to multiply -4 by x-1.
4x^{2}-4xy+y^{2}-4x^{2}-8xy+4x+8y
Use the distributive property to multiply -4x+4 by x+2y.
-4xy+y^{2}-8xy+4x+8y
Combine 4x^{2} and -4x^{2} to get 0.
-12xy+y^{2}+4x+8y
Combine -4xy and -8xy to get -12xy.
4x^{2}-4xy+y^{2}-4\left(x-1\right)\left(x+2y\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.
4x^{2}-4xy+y^{2}+\left(-4x+4\right)\left(x+2y\right)
Use the distributive property to multiply -4 by x-1.
4x^{2}-4xy+y^{2}-4x^{2}-8xy+4x+8y
Use the distributive property to multiply -4x+4 by x+2y.
-4xy+y^{2}-8xy+4x+8y
Combine 4x^{2} and -4x^{2} to get 0.
-12xy+y^{2}+4x+8y
Combine -4xy and -8xy to get -12xy.
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}