分解因式：（x的平方+4x+3)（x的平方+6x+8)-48=?

(x^2+4x+3)(x^2+6x+8)-48

=(x+1)(x+3)(x+2)(x+4)-48

=(x^2+5x+4)(x^2+5x+6-48)

=(x^+5x+4)^2+2(x^2+5x+4)-48

=(x^2+5x+4+8)(x^2+5x+4-6)

=(x^2+5x+12)(x^2+5x-2)

=(x+1)(x+3)(x+2)(x+4)-48
=(x^2+5x+4)(x^2+5x+6)-48
=(x^2+5x)^2+10(x^2+5x)-24
=(x^2+5x+12)(x^2+5x-2)

原式=(x+1)(x+3)(x+2)(x+4)-48
=[(x+1)(x+4)][(x+2)(x+3)]-48
=[(x²+5x)+4][(x²+5x)+6]-48
=(x²+5x)²-10(x²+5x)+24-48
=(x²+5x)²-10(x²+5x)-24
=(x²+5x-12)(x²+5x+2)

=(x+1)(x+3)(x+2)(x+4)-48
=(x^2+5x+4)(x^2+5x+6)-48
=(x^2+5x)^2+(x^2+5x)*10+24-48
=(x^2+5x)^2+(x^2+5x)*10-24
=(x^2+5x-2)(x^2+5x+12)