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4K^{2}+4K+1-2\left(4K-3\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2K+1\right)^{2}.
4K^{2}+4K+1-8K+6
Use the distributive property to multiply -2 by 4K-3.
4K^{2}-4K+1+6
Combine 4K and -8K to get -4K.
4K^{2}-4K+7
Add 1 and 6 to get 7.
4K^{2}+4K+1-2\left(4K-3\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2K+1\right)^{2}.
4K^{2}+4K+1-8K+6
Use the distributive property to multiply -2 by 4K-3.
4K^{2}-4K+1+6
Combine 4K and -8K to get -4K.
4K^{2}-4K+7
Add 1 and 6 to get 7.