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Question

Expand (x-1)4.


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Solution

Use the binomial theorem

We know that the binomial expansion of (x-a)n is given by C0xn+nC1nxn-1a1+C2xn-2a2+C3xn-3a3+n....+Cnx0annn

So using the above formula we will expand (x-1)4

Here,a=x and b=-1.

x-14=C0x4+4C14x3×(-1)1+C2x2×(-1)2+C3x(-1)3+4C4(-1)444.......(1)

We know that C0=C4=144,C1=C3=444 and C24=6

On substituting above values in the above equation 1, we get

x4-4x3+6x2-4x+1

Hence, the expansion of (x-1)4 is x4-4x3+6x2-4x+1


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