因式分解：(x^2+4x+6)(x^2+6x+6)-3x^2

原式 = [x^2 + 6 + 5x]^2 - x^2 - 3x^2 = [x^2 + 5x + 6]^2 - 4x^2
= (x^2 + 7x + 6)(x^2 - 3x + 6) = (x+1)(x+6)(x^2 - 3x + 6)

(x^2+4x+6)(x^2+6x+6)-3x^2
=[(x^2+5x+6)-x][x^2+5x+6)+x]-3x^2
=(x^2+5x+6)^2-4x^2
=(x^2+7x+6)(x^2+3x+6)
=(x+1)(x+6)(x^2+3x+6)
解法2
(x^2+4x+6)(x^2+6x+6)-3x^2
=[(x^2+6)+4x][(x^2+6)+6x]-3x^2
=(x^2+6)^2+10x(x^2+6)+21x^2
=[(x^2+6)+7x][(x^2+6)+3x]
=(x+1)(x+6)(x^2+3x+6)