(x+2)(x+3)(x+8)(x+12)-4x^2
=(x^2+5x+6)(x+8)(x+12)-4x^2
=(x^3+13x^2+46x+48)(x+12)-4x^2
=(x^4+25x^3+202x^2+600x+576)-4x^2
=x^4+25x^3+198x^2+600x+576