Using Binomial Theorem, evaluate (101)4

Asked by Pragya Singh | 1 year ago |  65

##### Solution :-

Given (101)4

101 can be expressed as the sum or difference of two numbers and then binomial theorem can be applied.

The given question can be written as 101 = 100 + 1

(101)4 = (100 + 1)4

4C0 (100)4 + 4C1 (100)3 (1) + 4C2 (100)2 (1)2 + 4C3 (100) (1)2 + 4C(1)4

= (100)4 + 4 (100)3 + 6 (100)2 + 4 (100) + (1)4

= 100000000 + 400000 + 60000 + 400 + 1

= 1040604001

Answered by Abhisek | 1 year ago

### Related Questions

#### Find the term independent of x in the expansion of (3/2 x2 – 1/3x)9

Find the term independent of x in the expansion of $$(\dfrac{3}{2x^2} – \dfrac{1}{3x})^9$$

#### Find the middle term in the expansion of (x – 1/x)2n+1

Find the middle term in the expansion of $$(x-\dfrac{ 1}{x})^{2n+1}$$

#### Find the middle term in the expansion of (1 + 3x + 3x2 + x3)2n

Find the middle term in the expansion of (1 + 3x + 3x2 + x3)2n

Find the middle term in the expansion of $$(\dfrac{x}{a} – \dfrac{a}{x})^{10}$$