Question

solve this by using binomial theorem (399)^⁴ and (203)^-³ ?​

Answer 1

Given :  399⁴  & (203)³  

To find : Solve using binomial theorem

Solution:

binomial theorem :

$(x + y)^n = \sum ^{n}C_{k} x^{n-k} y^k$    k = 0 to n

399⁴

= (400 - 1)⁴

= ⁴C₄400⁴(-1)⁰   + ⁴C₁400³(-1)   + ⁴C₂400²(-1)² +  ⁴C₃400¹(-1)³   + ⁴C₄400⁰(-1)⁴

= 25600000000  - 256000000  + 960000 - 1600  + 1

= 25344958401

399⁴= 25344958401

(203)³  

= (200 + 3)³

= ³C₀200³(3)⁰ + ³C₁200²(3)¹ + ³C₂200¹(3)² + ³C₃200⁰(3)³

= 8000000 +  360000  + 5400  + 27

=  8365427

(203)³   =  8365427  

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