(x+1)(x+2)(x+3)(x+4)
=(x+1)(x+4) (x+2)(x+3)
=(x^2+5x+4) (x^2+5x+6)
=[(x^2+5x)+4][ (x^2+5x+6]
=(x^2+5x)^2+4 (x^2+5x)+6(x^2+5x)+24
=(x^2+5x)^2+10(x^2+5x)+24
=x^4+10x^3+25x^2+10x^2+50x+24
=x^4+10x^3+35x^2+50x+24