Expansions for Positive Integral Index


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For n N, we have:

a) (a - b)n (a +(- b))n

Note 1:

It is advisable to remember the following values.

Note 2:

Working rules for expanding

(a + b)n, n N

Step 1:

The value of index, n implies that there will be n+1 terms in the expansion of (a + b)n.

Step 2:

Write the first term: nC0anb0.

Step 3:

For the second term, take coefficient as nC1, decreases the power of 'a' by 1 and increases the power of 'b' by 1. Thus,

the second term is nC1an-1b1.

Step 4:

For the third term, take coefficient as nC2, power of 'a' as n-2 and power of 'b' as 2. Continue this process repeatedly till the last term nCna0bn is obtained.



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