a: \(\left[\left(3x-2\right)\left(x+1\right)-\left(2x+5\right)\left(x^2-1\right)\right]:\left(x+1\right)\)
\(=\dfrac{\left(3x-2\right)\left(x+1\right)-\left(2x+5\right)\left(x-1\right)\left(x+1\right)}{x+1}\)
\(=3x-2-\left(2x+5\right)\left(x-1\right)\)
\(=3x-2-\left(2x^2-2x+5x-5\right)\)
\(=3x-2-\left(2x^2+3x-5\right)\)
\(=3x-2-2x^2-3x+5=-2x^2+3\)
b: \(\left(2x+1\right)^2-2\left(2x+1\right)\left(3-x\right)+\left(3-x\right)^2\)
\(=\left[\left(2x+1\right)-\left(3-x\right)\right]^2\)
\(=\left(2x+1-3+x\right)^2\)
\(=\left(3x-2\right)^2=9x^2-12x+4\)
c: \(\left(x-1\right)^3-\left(x+1\right)\left(x^2-x+1\right)-\left(3x+1\right)\left(1-3x\right)\)
\(=x^3-3x^2+3x-1-\left(x^3+1\right)+\left(3x+1\right)\left(3x-1\right)\)
\(=x^3-3x^2+3x-1-x^3-1+9x^2-1\)
\(=6x^2+3x-3\)
