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x^{2}+2x+1-8\left(x-1\right)+16
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+1-8x+8+16
Use the distributive property to multiply -8 by x-1.
x^{2}-6x+1+8+16
Combine 2x and -8x to get -6x.
x^{2}-6x+9+16
Add 1 and 8 to get 9.
x^{2}-6x+25
Add 9 and 16 to get 25.
x^{2}+2x+1-8\left(x-1\right)+16
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+1-8x+8+16
Use the distributive property to multiply -8 by x-1.
x^{2}-6x+1+8+16
Combine 2x and -8x to get -6x.
x^{2}-6x+9+16
Add 1 and 8 to get 9.
x^{2}-6x+25
Add 9 and 16 to get 25.