Question

evaLuAte using binomial theorem:

(10.01) whole power 3 to 3 places of decimal......??​

Answer 1

Answer:

1003.003 is the answer

Step-by-step explanation:

Answer 2

The answer is (10.03)³ = 1003.003001

Given: (10.01)³

To find: Evaluating (10.01)³using binomial theorem

Solution: According to the Binomial expansion theorem,

the Binomial expansion formula is given  by

(x+y)ⁿ = xⁿ + nxⁿ⁻1y¹ + n(n−1)2! xⁿ⁻²y² +…….+ yⁿ

If take n = 3 then the formula will be

(x + y)³ = x³ + 3x²y + 3xy² + y³  

Here we can write give term (10.01)³ = (10+0.01)³

therefore, (10 + 0.01)³ = 10³ + 3(10)²(0.01) + 3(10)(0.01)² + (0.01)³ 

= 1000 + 3(100)(0.01) + 3(10)(0.0001) + 0.000001   

= 1000 + 3(1) + 3(0.001) + 0.000001

= 1000 +3 + 0.003 + 0.000001

= 1003.003 + 0.000001  

= 1003.003001  or  1003.003 + 10⁻⁶      [∵ 0.000001 = 10⁻⁶]  

     (10.03)³ = 1003.003001

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