Evaluate
-2x^{2}-y^{2}
Expand
-2x^{2}-y^{2}
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2x^{2}-4xy-\left(2x-y\right)^{2}
Use the distributive property to multiply 2x by x-2y.
2x^{2}-4xy-\left(4x^{2}-4xy+y^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.
2x^{2}-4xy-4x^{2}+4xy-y^{2}
To find the opposite of 4x^{2}-4xy+y^{2}, find the opposite of each term.
-2x^{2}-4xy+4xy-y^{2}
Combine 2x^{2} and -4x^{2} to get -2x^{2}.
-2x^{2}-y^{2}
Combine -4xy and 4xy to get 0.
2x^{2}-4xy-\left(2x-y\right)^{2}
Use the distributive property to multiply 2x by x-2y.
2x^{2}-4xy-\left(4x^{2}-4xy+y^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.
2x^{2}-4xy-4x^{2}+4xy-y^{2}
To find the opposite of 4x^{2}-4xy+y^{2}, find the opposite of each term.
-2x^{2}-4xy+4xy-y^{2}
Combine 2x^{2} and -4x^{2} to get -2x^{2}.
-2x^{2}-y^{2}
Combine -4xy and 4xy to get 0.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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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}