Evaluate
x^{2}+32xy+13y^{2}
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x^{2}+32xy+13y^{2}
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4x^{2}+20xy+25y^{2}-3\left(x-2y\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+5y\right)^{2}.
4x^{2}+20xy+25y^{2}-3\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}.
4x^{2}+20xy+25y^{2}-3x^{2}+12xy-12y^{2}
Use the distributive property to multiply -3 by x^{2}-4xy+4y^{2}.
x^{2}+20xy+25y^{2}+12xy-12y^{2}
Combine 4x^{2} and -3x^{2} to get x^{2}.
x^{2}+32xy+25y^{2}-12y^{2}
Combine 20xy and 12xy to get 32xy.
x^{2}+32xy+13y^{2}
Combine 25y^{2} and -12y^{2} to get 13y^{2}.
4x^{2}+20xy+25y^{2}-3\left(x-2y\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+5y\right)^{2}.
4x^{2}+20xy+25y^{2}-3\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}.
4x^{2}+20xy+25y^{2}-3x^{2}+12xy-12y^{2}
Use the distributive property to multiply -3 by x^{2}-4xy+4y^{2}.
x^{2}+20xy+25y^{2}+12xy-12y^{2}
Combine 4x^{2} and -3x^{2} to get x^{2}.
x^{2}+32xy+25y^{2}-12y^{2}
Combine 20xy and 12xy to get 32xy.
x^{2}+32xy+13y^{2}
Combine 25y^{2} and -12y^{2} to get 13y^{2}.
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