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4x^{2}-\left(4x^{2}+4x+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.
4x^{2}-4x^{2}-4x-1
To find the opposite of 4x^{2}+4x+1, find the opposite of each term.
-4x-1
Combine 4x^{2} and -4x^{2} to get 0.
4x^{2}-\left(4x^{2}+4x+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.
4x^{2}-4x^{2}-4x-1
To find the opposite of 4x^{2}+4x+1, find the opposite of each term.
-4x-1
Combine 4x^{2} and -4x^{2} to get 0.