a: \(=x^2\left(2x+1\right)-4\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x-2\right)\left(x+2\right)\)
b: \(=x^2\left(2x+3\right)+\left(2x+3\right)=\left(2x+3\right)\left(x^2+1\right)\)
c: \(=x\left(x^2+2xy+y^2-4\right)\)
\(=x\left(x+y+2\right)\left(x+y-2\right)\)
d: \(=\left(8a^3-b^3\right)+2ab\left(2a-b\right)\)
\(=\left(2a-b\right)\left(4a^2+2ab+b^2\right)+2ab\left(2a-b\right)\)
\(=\left(2a-b\right)\left(2a+b\right)^2\)
e: \(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)
\(A=x^2\left(2x+1\right)-4\left(2x+1\right)=\left(2x+1\right)\left(x^2-4\right)=\left(2x+1\right)\left(x+2\right)\left(x-2\right)\)
\(B=x^2\left(2x+3\right)+\left(2x+3\right)=\left(2x+3\right)\left(x^2+1\right)\)
\(C=x\left(x^2+2xy+y^2-4\right)=x\left[\left(x+y\right)^2-4\right]=x\left(x+y+4\right)\left(x+y-4\right)\)
\(D=4a^2\left(2a+b\right)-b^2\left(2a+b\right)=\left(2a+b\right)\left(4a^2-b^2\right)=\left(2a+b\right)^2\left(2a-b\right)\)
\(E=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)
