计算(x+1)(x+2)(x+3)(x+4)

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计算(x+1)(x+2)(x+3)(x+4)
计算(x+1)(x+2)(x+3)(x+4)

计算(x+1)(x+2)(x+3)(x+4)
(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

x的四次+10x的三次+36x的二次+57x+36


(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)^2+10(x^2+5x)+24
=x^4+10x^3+25x^2+10x^2+50x+24=x^4+10x^3+35x^2+50x+24

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