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4x^{2}
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4x^{2}
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x^{2}-xy+\frac{1}{4}y^{2}+\left(x+\frac{1}{2}y\right)^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{2}y\right)^{2}.
x^{2}-xy+\frac{1}{4}y^{2}+x^{2}+xy+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{2}y\right)^{2}.
2x^{2}-xy+\frac{1}{4}y^{2}+xy+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}+\frac{1}{4}y^{2}+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Combine -xy and xy to get 0.
2x^{2}+\frac{1}{2}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Combine \frac{1}{4}y^{2} and \frac{1}{4}y^{2} to get \frac{1}{2}y^{2}.
2x^{2}+\frac{1}{2}y^{2}+\left(2x-y\right)\left(x+\frac{1}{2}y\right)
Use the distributive property to multiply 2 by x-\frac{1}{2}y.
2x^{2}+\frac{1}{2}y^{2}+2x^{2}-\frac{1}{2}y^{2}
Use the distributive property to multiply 2x-y by x+\frac{1}{2}y and combine like terms.
4x^{2}+\frac{1}{2}y^{2}-\frac{1}{2}y^{2}
Combine 2x^{2} and 2x^{2} to get 4x^{2}.
4x^{2}
Combine \frac{1}{2}y^{2} and -\frac{1}{2}y^{2} to get 0.
x^{2}-xy+\frac{1}{4}y^{2}+\left(x+\frac{1}{2}y\right)^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{2}y\right)^{2}.
x^{2}-xy+\frac{1}{4}y^{2}+x^{2}+xy+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{2}y\right)^{2}.
2x^{2}-xy+\frac{1}{4}y^{2}+xy+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}+\frac{1}{4}y^{2}+\frac{1}{4}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Combine -xy and xy to get 0.
2x^{2}+\frac{1}{2}y^{2}+2\left(x-\frac{1}{2}y\right)\left(x+\frac{1}{2}y\right)
Combine \frac{1}{4}y^{2} and \frac{1}{4}y^{2} to get \frac{1}{2}y^{2}.
2x^{2}+\frac{1}{2}y^{2}+\left(2x-y\right)\left(x+\frac{1}{2}y\right)
Use the distributive property to multiply 2 by x-\frac{1}{2}y.
2x^{2}+\frac{1}{2}y^{2}+2x^{2}-\frac{1}{2}y^{2}
Use the distributive property to multiply 2x-y by x+\frac{1}{2}y and combine like terms.
4x^{2}+\frac{1}{2}y^{2}-\frac{1}{2}y^{2}
Combine 2x^{2} and 2x^{2} to get 4x^{2}.
4x^{2}
Combine \frac{1}{2}y^{2} and -\frac{1}{2}y^{2} to get 0.
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Limits
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