Binomial Theorem

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Q1. Find the coefficient of x^5 in the expansion of (2x - 3)^8.

Solution:

The coefficient of x^5 is C(8,5) * (2)^5 * (-3)^3 = 56 * 32 * (-27) = -6720.

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Q2. What is the value of the term containing x^5 in the expansion of (x + 2)^8? (2020)

Solution:

The term containing x^5 is C(8,5)(2)^3 = 56 * 8 = 448.

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Q3. What is the 3rd term in the expansion of (2x - 3)^5? (2022)

Solution:

The 3rd term is C(5,2) * (2x)^3 * (-3)^2 = 10 * 8x^3 * 9 = -720x^3.

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Q4. Find the term containing x^3 in the expansion of (x - 1)^5.

Solution:

The term containing x^3 is C(5,3) * x^3 * (-1)^2 = 10 * x^3 * 1 = 10.

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Q5. In the expansion of (2x - 5)^5, what is the coefficient of x^2? (2021)

Solution:

The coefficient of x^2 is C(5,2) * (2)^2 * (-5)^3 = 10 * 4 * (-125) = -5000.

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Q6. Find the coefficient of x^5 in the expansion of (2x - 3)^6. (2022)

Solution:

The coefficient of x^5 is C(6,5) * (2)^5 * (-3)^1 = 6 * 32 * (-3) = -576.

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Q7. Calculate the coefficient of x^2 in the expansion of (x + 4)^6.

Solution:

The coefficient of x^2 is given by C(6,2) * 4^4 = 15 * 256 = 3840.

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Q8. Find the coefficient of x^2 in the expansion of (x - 5)^5.

Solution:

The coefficient of x^2 is C(5,2) * (-5)^3 = 10 * (-125) = -1250.

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Q9. What is the 3rd term in the expansion of (x + 2)^5? (2021)

Solution:

The 3rd term is given by C(5,2) * (x)^3 * (2)^2 = 10 * x^3 * 4 = 40.

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Q10. What is the coefficient of x^2 in the expansion of (2x + 1)^6?

Solution:

The coefficient of x^2 is C(6,2) * (2)^2 * (1)^4 = 15 * 4 = 60.