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# Binomial Theorem

### Binomial theorem is a theorem developed for calculating any power of any binomial without actually multiplying at length.

General binomial expansion is denoted by

(a+b)=nc0an +nc1an-1b+nc2an-2b2+…………………..+ncn-1abn-1+ncnbn  where n>=0 and

Example (x+y)3=3c0x3+3c1x2y+3c2xy2+3c2y3

Example – Expand (p+1)3

(p+1)3=3c0*p3+3c1*p2*1+3c2*p*12+3c2*13

=  p3+3p2+3p+1

#### Some Facts about Binomial Theorem

• General term for an expansion (a+b)n is Tr+1 =ncran-rbis , where 0 <= r<= n.
• Number of terms in expansion will be n + 1.

## Check Point:

Expand the following binomials –

1) (a+b)3

2) (s+3)3

3) (y2+1)4

4) (3+x)4

5) (z+2)6

1) a3+3a2b+3b2a+b3

2)  s3+9s2+27s+27

3) y8+4y6+6y4+4y2+1

4) 81+108x+54x2+12x3+x4

5) z6+12z5+60z4+160z3+240z2+192z+64

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