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