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4x^{2}-4xy+y^{2}-\left(y-2x\right)^{2}+\left(2x+7\right)^{3}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.
4x^{2}-4xy+y^{2}-\left(y^{2}-4yx+4x^{2}\right)+\left(2x+7\right)^{3}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-2x\right)^{2}.
4x^{2}-4xy+y^{2}-y^{2}+4yx-4x^{2}+\left(2x+7\right)^{3}
To find the opposite of y^{2}-4yx+4x^{2}, find the opposite of each term.
4x^{2}-4xy+4yx-4x^{2}+\left(2x+7\right)^{3}
Combine y^{2} and -y^{2} to get 0.
4x^{2}-4x^{2}+\left(2x+7\right)^{3}
Combine -4xy and 4yx to get 0.
0+\left(2x+7\right)^{3}
Combine 4x^{2} and -4x^{2} to get 0.
0+8x^{3}+84x^{2}+294x+343
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x+7\right)^{3}.
343+8x^{3}+84x^{2}+294x
Add 0 and 343 to get 343.
4x^{2}-4xy+y^{2}-\left(y-2x\right)^{2}+\left(2x+7\right)^{3}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.
4x^{2}-4xy+y^{2}-\left(y^{2}-4yx+4x^{2}\right)+\left(2x+7\right)^{3}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-2x\right)^{2}.
4x^{2}-4xy+y^{2}-y^{2}+4yx-4x^{2}+\left(2x+7\right)^{3}
To find the opposite of y^{2}-4yx+4x^{2}, find the opposite of each term.
4x^{2}-4xy+4yx-4x^{2}+\left(2x+7\right)^{3}
Combine y^{2} and -y^{2} to get 0.
4x^{2}-4x^{2}+\left(2x+7\right)^{3}
Combine -4xy and 4yx to get 0.
0+\left(2x+7\right)^{3}
Combine 4x^{2} and -4x^{2} to get 0.
0+8x^{3}+84x^{2}+294x+343
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x+7\right)^{3}.
343+8x^{3}+84x^{2}+294x
Add 0 and 343 to get 343.