\(a)\left(x+1\right)^2\cdot\left(x-1\right)^2=\left(x+1\right)\left(x+1\right)\left(x-1\right)\left(x-1\right)\)
\(=\left(x^2-1\right)\left(x^2-1\right)=\left(x^2-1\right)^2\)
\(b)4x\left(x-3\right)\cdot\left(x+3\right)-\left(2x-1\right)^2=4x\left(x^2-9\right)-\left(2x-1\right)^2\)
\(=4x^3-36x-\left(4x^2-4x+1\right)\)
\(=4x^3-36x-4x^2+4x-1\)
\(=4x^3-4x^2-32x-1\)
\(c)\left(x-1\right)^3-4x\left(x-1\right)\left(1+x\right)+3\left(x-1\right)\left(x^2+x+1\right)\)
\(=x^3-3x^2+3x-1-\left(4x^2-4x\right)\left(1+x\right)+3\left(x^3-1\right)\)
\(=x^3-3x^2+3x-1-4x^2-4x^3+4x+4x^2+3x^3-3\)
\(=-3x^2+7x-4\)
