Factor x^4+a^2x^2+b^2x^2+a^2b^2

$x^{4} + a^{2} x^{2} + b^{2} x^{2} + a^{2} b^{2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{4} + a^{2} x^{2}) + b^{2} x^{2} + a^{2} b^{2}$

Factor out the greatest common factor (GCF) from each group.

$x^{2} (x^{2} + a^{2}) + b^{2} (x^{2} + a^{2})$

Factor the polynomial by factoring out the greatest common factor, $x^{2} + a^{2}$ .

$(x^{2} + a^{2}) (x^{2} + b^{2})$