Evaluate
4xy-8y^{2}-4y-1
Expand
4xy-8y^{2}-4y-1
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x^{2}-4y^{2}-4y-1-\left(x-2y\right)^{2}
Use the distributive property to multiply x+2y+1 by x-2y-1 and combine like terms.
x^{2}-4y^{2}-4y-1-\left(x^{2}-4xy+4y^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2y\right)^{2}.
x^{2}-4y^{2}-4y-1-x^{2}+4xy-4y^{2}
To find the opposite of x^{2}-4xy+4y^{2}, find the opposite of each term.
-4y^{2}-4y-1+4xy-4y^{2}
Combine x^{2} and -x^{2} to get 0.
-8y^{2}-4y-1+4xy
Combine -4y^{2} and -4y^{2} to get -8y^{2}.
x^{2}-4y^{2}-4y-1-\left(x-2y\right)^{2}
Use the distributive property to multiply x+2y+1 by x-2y-1 and combine like terms.
x^{2}-4y^{2}-4y-1-\left(x^{2}-4xy+4y^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2y\right)^{2}.
x^{2}-4y^{2}-4y-1-x^{2}+4xy-4y^{2}
To find the opposite of x^{2}-4xy+4y^{2}, find the opposite of each term.
-4y^{2}-4y-1+4xy-4y^{2}
Combine x^{2} and -x^{2} to get 0.
-8y^{2}-4y-1+4xy
Combine -4y^{2} and -4y^{2} to get -8y^{2}.
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Limits
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