Evaluate
x^{2}-xy-4y^{2}
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x^{2}-xy-4y^{2}
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3x^{2}-5xy-2y^{2}-2\left(x-y\right)^{2}
Use the distributive property to multiply 3x+y by x-2y and combine like terms.
3x^{2}-5xy-2y^{2}-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}.
3x^{2}-5xy-2y^{2}-2x^{2}+4xy-2y^{2}
Use the distributive property to multiply -2 by x^{2}-2xy+y^{2}.
x^{2}-5xy-2y^{2}+4xy-2y^{2}
Combine 3x^{2} and -2x^{2} to get x^{2}.
x^{2}-xy-2y^{2}-2y^{2}
Combine -5xy and 4xy to get -xy.
x^{2}-xy-4y^{2}
Combine -2y^{2} and -2y^{2} to get -4y^{2}.
3x^{2}-5xy-2y^{2}-2\left(x-y\right)^{2}
Use the distributive property to multiply 3x+y by x-2y and combine like terms.
3x^{2}-5xy-2y^{2}-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}.
3x^{2}-5xy-2y^{2}-2x^{2}+4xy-2y^{2}
Use the distributive property to multiply -2 by x^{2}-2xy+y^{2}.
x^{2}-5xy-2y^{2}+4xy-2y^{2}
Combine 3x^{2} and -2x^{2} to get x^{2}.
x^{2}-xy-2y^{2}-2y^{2}
Combine -5xy and 4xy to get -xy.
x^{2}-xy-4y^{2}
Combine -2y^{2} and -2y^{2} to get -4y^{2}.
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Limits
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