Jasonbradley
Home

(3/2x+1)3 In Expanded Form

2 min read Jun 16, 2024
(3/2x+1)3 In Expanded Form

Expanding (3/2x + 1)³

In this article, we'll expand the expression (3/2x + 1)³ using the binomial theorem.

Understanding the Binomial Theorem

The binomial theorem provides a formula for expanding any expression of the form (a + b)ⁿ, where 'n' is a positive integer. The theorem states:

(a + b)ⁿ = aⁿ + naⁿ⁻¹b + (n(n-1)/2!)aⁿ⁻²b² + (n(n-1)(n-2)/3!)aⁿ⁻³b³ + ... + bⁿ

Where '!' represents the factorial (e.g., 5! = 5 * 4 * 3 * 2 * 1).

Applying the Theorem

Let's apply the binomial theorem to our expression (3/2x + 1)³:

  1. Identify 'a' and 'b':

    • a = 3/2x
    • b = 1

  2. Identify 'n':

    • n = 3

  3. Substitute into the formula: (3/2x + 1)³ = (3/2x)³ + 3(3/2x)²(1) + 3(3/2x)(1)² + (1)³

  4. Simplify: (3/2x + 1)³ = 27/8x³ + 27/4x² + 9/2x + 1

The Expanded Form

Therefore, the expanded form of (3/2x + 1)³ is 27/8x³ + 27/4x² + 9/2x + 1.

Related Post

Featured Posts