因为(1＋x)^5*(1-x)^4
=[(1+x)(1-x)]^4*(1+x)
=(1-x^2)^4*(1+x)
=[(1-x^2)^2]^2*(1+x)
=(1-2x^2+x^4)^2*(1+x)
=(1+4x^4+x^8-4x^2+2x^4-4x^6)*(1+x)
=(x^8-4x^6+6x^4-4x^2+1)*(x+1)
=x^9-4x^7+6x^5-4x^3+x+x^8-4x^6+6x^4-4x^2+1,
所以在(1＋x)^5*(1-x)^4的展开式中,x^3的系数为-4.