If n is a positive integer, (a + x)^{n} can be expanded as

- (a + x)
^{n}= a^{n}+^{n}C_{1}a^{n-1}x +^{n}C_{2}a^{n-2}x^{2}+^{n}C_{3}a^{n-3}x^{3}+ ... + x^{n}.Suggested Action:###### Applying binomial on (a + b)

^{2}Using general expansion equation:

a^{2-0}+_{2}c^{1}(a)^{2-1}(b)^{1}+ b^{2-0}= a^{2}+2ab+ b^{2}###### Applying Binomial on (a + b)

^{3}a^{3-0}+^{3}c_{1}a^{3-1}b^{1}+^{3}c_{2}a^{3-2}b^{2}+ b^{3-0}= a^{3}+ 3a^{2}b + 3ab^{2}+ b^{3}And if in this case if particular term say ‘r’ is asked, then instead of applying the whole expansion, the following direct formula can be applied to find the ‘r’th term - ‘r’th term = x
^{n–r+1}a^{r – 1}[{n(n – 1)(n – 2) ... (n – r + 2)} ÷ (r – 1)!]. Similarly (x + a)^{n}can be expanded as - (x + a)
^{n}= x^{n}+^{n}C_{1}x^{n–1}a +^{n}C_{1}x^{n–2}a^{2}+^{n}C_{1}x^{n–3}a^{3}+ ... + a^{n}In case of a binomial expansion, if any particular term say ‘r’ is asked, then instead of applying the whole expansion, the following direct formula can be applied to find the ‘r’th term. - ‘r’th term = a
^{n–r+1}x^{r–1}[{n(n–1) (n – 2) ... (n – r + 2)} ÷ (r – 1)!] So order of the term to be expanded is very important i.e., whether it is in the form (a + x)^{n}or (x + a)^{n}

Suggested Action: