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Question

How do you use the binomial formula to expand (x+1)3


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Solution

Expand (x+1)3

Binomial formula to expand a+b3 is

a+b3=C03a3b0+C13a2b1+C23a1b2+C33a0b3

Here we have, a=x and b=1

Substituting the values of a and b we get

x+13=C03x310+C13x211+C23x112+C33x013

x+13=3!0!3!x310+3!1!2!x211+3!2!1!x112+3!3!0!x013 ...[Cr=n!r!n-r!n]

x+13=x3+3x2+3x+1

Hence the expansion of (x+1)3 using binomial theorem is x3+3x2+3x+1


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