a, \(x^4+2x^2-3\)\(=\left[\left(x^2\right)^2+2.x^2.1+1\right]-\left(1-3\right)\)
\(=\left(x^2+1\right)^2-\left(\sqrt{2}\right)^2\)
\(=\left(x^2+1-\sqrt{1}\right)\left(x^2+1+\sqrt{2}\right)\)
b,\(\left(x^2+2x\right)\left(x^2+2x+4\right)+3=x^4+2x^3+4x^2+2x^3+4x^2+8x\)
\(=\left(x^4+4x^3\right)+\left(8x^2+8x\right)=x\left(x^3+4x^2\right)+x\left(8x+8\right)\)
\(=x\left(x^3+4x^2+8x+8\right)\)
c,\(2xy^2+4xy+2x-2xz^2+4xzt-2xt^2\)
\(=\left(2xy^2+4xy\right)+\left(2x-2xz^2\right)+\left(4xzt-2xt^2\right)\)
\(=2x\left(y^2+2y\right)+2x\left(1-z^2\right)+2x\left(2zt-t^2\right)\)
\(=2x\left(y^2+2y+1-z^2+2zt-t^2\right)\)
\(=2x\left[\left(y^2+2y+1\right)-\left(z^2-2zt+t^2\right)\right]\)
\(=2x\left[\left(y+1\right)^2-\left(z-t\right)^2+\left(2y-t^2\right)\right]\)
\(=2x\left[\left(y+1-z-t\right)\left(y+1+z-t\right)\right]\)
