In the expansion of (1 + x) 5 (1-x) 4, the coefficient of X3 is In the expansion of (1 + x) 5 (1-x) 4, the coefficient of X3 is________ 3l, how does C43 (1-x2) * (1 + x) = - 4x3 + 4 come from

In the expansion of (1 + x) 5 (1-x) 4, the coefficient of X3 is In the expansion of (1 + x) 5 (1-x) 4, the coefficient of X3 is________ 3l, how does C43 (1-x2) * (1 + x) = - 4x3 + 4 come from

Because (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,
So in the expansion of (1 + x) ^ 5 * (1-x) ^ 4, the coefficient of x ^ 3 is - 4

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