Evaluate
-7x^{2}+12xy-5y^{2}-30002
Expand
-7x^{2}+12xy-5y^{2}-30002
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-30002-x^{2}+y^{2}-6\left(x-y\right)^{2}
To find the opposite of x^{2}-y^{2}, find the opposite of each term.
-30002-x^{2}+y^{2}-6\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}.
-30002-x^{2}+y^{2}-6x^{2}+12xy-6y^{2}
Use the distributive property to multiply -6 by x^{2}-2xy+y^{2}.
-30002-7x^{2}+y^{2}+12xy-6y^{2}
Combine -x^{2} and -6x^{2} to get -7x^{2}.
-30002-7x^{2}-5y^{2}+12xy
Combine y^{2} and -6y^{2} to get -5y^{2}.
-30002-x^{2}+y^{2}-6\left(x-y\right)^{2}
To find the opposite of x^{2}-y^{2}, find the opposite of each term.
-30002-x^{2}+y^{2}-6\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}.
-30002-x^{2}+y^{2}-6x^{2}+12xy-6y^{2}
Use the distributive property to multiply -6 by x^{2}-2xy+y^{2}.
-30002-7x^{2}+y^{2}+12xy-6y^{2}
Combine -x^{2} and -6x^{2} to get -7x^{2}.
-30002-7x^{2}-5y^{2}+12xy
Combine y^{2} and -6y^{2} to get -5y^{2}.
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