(a^2x^2 + 2abx + b^2) + (c^2x^2 + 2cdx + d^2)
(a^2x^2 + c^2x^2) + 2abx + 2cdx + (b^2 + d^2)
(a^2 + c^2)x^2 + 2(ab + cd)x + (b^2 + d^2)
((a^2 + c^2)x^2 + 2(ab + cd)x) + (b^2 + d^2)
((a^2 + c^2)x + (ab + cd))^2 + (b^2 + d^2 - (ab + cd)^2)
(a^2x^2 + 2abx + b^2) + (c^2x^2 + 2cdx + d^2)
(a^2x^2 + c^2x^2) + 2abx + 2cdx + (b^2 + d^2)
(a^2 + c^2)x^2 + 2(ab + cd)x + (b^2 + d^2)
((a^2 + c^2)x^2 + 2(ab + cd)x) + (b^2 + d^2)
((a^2 + c^2)x + (ab + cd))^2 + (b^2 + d^2 - (ab + cd)^2)