\(=x^2y^2+8xyab+16a^2b^2+4a^2y^2-8xyab+4b^2x^2\)
\(=x^2y^2+4a^2y^2+4b^2x^2+16a^2b^2\)
\(=\left(x^2y^2+4b^2x^2\right)+\left(4a^2y^2+16a^2b^2\right)\)
\(=x^2\left(4b^2+y^2\right)+4a^2\left(y^2+4b^2\right)\)
\(=\left(4b^2+y^2\right)\left(x^2+4a^2\right)\)