Question

Using binominal theorem, evaluate each of the following : 

(i) (101)⁴ 

(ii) (98)⁴ 

(iii)(1.2)⁴

Answer 1

(i) (101)⁴ 

To find: Value of (101)⁴ 

Formula used: (i)

ⁿC_r = \(\frac{n!}{(n-r)!(r)!}\)

(ii) (a+b)ⁿ = ⁿC₀aⁿ + ⁿC₁a^n-1b + ⁿC₂a^n-2b² + … +ⁿC_n-1ab^n-1 + ⁿC_nbⁿ 

101 = (100+1) 

Now (101)⁴ = (100+1)⁴ 

(100+1)⁴ =

= 104060401

(ii) (98)⁴ 

To find: Value of (98)⁴

Formula used: (i)

ⁿC_r = \(\frac{n!}{(n-r)!(r)!}\)

(ii) (a+b)ⁿ = ⁿC₀aⁿ + ⁿC₁a^n-1b + ⁿC₂a^n-2b² + … +ⁿC_n-1ab^n-1 + ⁿC_nbⁿ 

98 = (100-2) 

Now (98)⁴ = (100-2)⁴ 

(100-2)⁴

= 92236816

(iii) (1.2)⁴ 

To find: Value of (1.2)⁴

Formula used: (i)

ⁿC_r = \(\frac{n!}{(n-r)!(r)!}\)

(ii) (a+b)ⁿ = ⁿC₀aⁿ + ⁿC₁a^n-1b + ⁿC₂a^n-2b² + … +ⁿC_n-1ab^n-1 + ⁿC_nbⁿ 

1.2 = (1 + 0.2) 

Now (1.2)⁴ = (1 + 0.2)⁴ 

(1+0.2)⁴

= 2.0736