Question 6 of 20intermediate🔧 ApplyNumerical4 marks

Using binomial theorem, evaluate each of the following: (96)^3

Correct Answer

884736

Exercise: EXERCISE 7.1 | Q: 6 | (Page 8)
For More Understanding

Explanation

Following the method shown in Example 2 of the textbook, we express 96 as the difference of two numbers (100 - 4) where powers are easier to calculate. Then we apply the binomial theorem expansion for (a - b)³. The binomial coefficients for n=3 are: ³C₀=1, ³C₁=3, ³C₂=3, ³C₃=1. After expanding and simplifying all terms, we get the final answer 884736.

Solution Steps

  1. Step 1: Express 96 as (100 - 4)

  2. Step 2: Apply binomial theorem: (96)³ = (100 - 4)³

  3. Step 3: Expand using formula: = ³C₀(100)³ - ³C₁(100)²(4) + ³C₂(100)(4)² - ³C₃(4)³

  4. Step 4: Substitute binomial coefficients: = 1×(100)³ - 3×(100)²×4 + 3×(100)×16 - 1×641 \times 64

  5. Step 5: Calculate each term: = 1000000 - 120000 + 4800 - 64

  6. Step 6: Simplify: = 1000000 - 120000 + 4800 - 64 = 884736

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