a(x-x_1)^2(x-x_2)^2 = \\
a x^4 + a x^3 (-2 x_1 - 2 x_2) + 
 a x^2 (x_1^2 + 4 x_1 x_2 + x_2^2) + a x (-2 x_1^2 x_2 - 2 x_1 x_2^2)+ a x_1^2 x_2^2.