Question

Use the Binomial Theorem to find the coefficient of x⁷ in the expansion of (3x−1)¹⁰.

a) 42
b) 120
c) 210
d) 252

Answer 1

The coefficient of x⁷ in the expansion of (3x−1)¹⁰ using the Binomial Theorem is 120.

Step-by-step explanation:

To find the coefficient of x⁷ in the expansion of (3x−1)¹⁰ using the Binomial Theorem, we can first expand the binomial using the formula:

(a + b)ⁿ = nC₀aⁿb⁰ + nC₁aⁿ⁻¹b¹ + nC₂aⁿ⁻²b² + ... + nCₙa⁰bⁿ

In this case, a = 3x and b = -1, and n = 10. So, the coefficient of x⁷ will be given by the term nC₇(3x)³(1)⁷. Plugging the values into the formula, we get:

nC₇ = 10C₇ = 10!/7!(10-7)! = 10!/(7!3!) = 10 × 9 × 8/(3 × 2 × 1) = 120

So, the coefficient of x⁷ is 120.