\(\left(x+3\right)^2-\left(x+1\right)\left(x-1\right)-10\left(x+2\right)+1\)
\(=\left(x^2+6x+9\right)-\left(x^2-1\right)-\left(10x+20\right)+1\)
\(=x^2+6x+9-x^2+1-10x-20+1\)
\(=\left(x^2-x^2\right)+\left(6x-10x\right)+\left(9+1-20+1\right)\)
\(=-4x-9\)
`= x^2 + 6x + 9 - x^2 + 1 - 10x - 20 + 1`
`= -4x - 9`