Help me out! Factor the polynomial if possible.?

m^2(x^2+y^2) + d^2(x^2+y^2)=(d^2+m^2)(x^2+y^2)

(m^2 + d^2)(x^2 + y^2) I don't know of any formulas or systems for doing this kind of factoring. You just have to study the polynomial and take it apart piece by piece.

m^2x^2 + d^2y^2 + d^2x^2 + m^2y^2
= m^2x^2 + m^2y^2 + d^2x^2 + d^2y^2
= (m^2x^2 + m^2y^2) + (d^2x^2 + d^2y^2)
= m^2(x^2 + y^2) + d^2(x^2 + y^2)
= (x^2 + y^2)(m^2 + d^2)