Answer :

To Find : Coefficients of x4


For (1+x)n


a=1, b=x


We have a formula,





For (1-x)n


a=1, b=-x and n=n


We have formula,







Coefficients of x4 are


x0.x4 = C0C4


x1.x3 = - C1C3


x2.x2 = C2C2


x3.x1= - C3C1


x4.x0 = C4C0


Therefore, Coefficient of x4


= C4C0 - C1C3 + C2C2 - C3C1 + C4C0


Let us assume, n=4, it becomes


4C4 4C0 - 4C1 4C3 + 4C2 4C2 - 4C3 4C1 + 4C4 4C0


We know that ,



By using above formula, we get,


4C4 4C0 - 4C1 4C3 + 4C2 4C2 - 4C3 4C1 + 4C4 4C0


= (1)(1) – (4)(4) + (6)(6) – (4)(4) + (1)(1)


= 1 – 16 + 36 – 16 + 1


= 6


= 4C2


Therefore, in general,


C4C0 - C1C3 + C2C2 - C3C1 + C4C0 = C2


Therefore, Coefficient of x4 = C2


Conclusion :


• Coefficient of x4 = C2


• C4C0 - C1C3 + C2C2 - C3C1 + C4C0 = C2


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