My Learning Cart
?
Categories
Account

In the expansion of (2x + 3)^4, what is the coefficient of x^1?

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: In the expansion of (2x + 3)^4, what is the coefficient of x^1?

Options:

  1. 72
  2. 48
  3. 36
  4. 24

Correct Answer: 48

Solution: 

The coefficient of x^1 is C(4,1) * (2)^1 * (3)^3 = 4 * 2 * 27 = 216.

In the expansion of (2x + 3)^4, what is the coefficient of x^1?

Practice Questions

Q1
In the expansion of (2x + 3)^4, what is the coefficient of x^1?
  1. 72
  2. 48
  3. 36
  4. 24

Questions & Step-by-Step Solutions

In the expansion of (2x + 3)^4, what is the coefficient of x^1?
Correct Answer: 216
  • Step 1: Identify the expression to expand, which is (2x + 3)^4.
  • Step 2: Recognize that we need to find the coefficient of x^1 in the expansion.
  • Step 3: Use the Binomial Theorem, which states that (a + b)^n = Σ (C(n, k) * a^(n-k) * b^k) for k = 0 to n.
  • Step 4: In our case, a = 2x, b = 3, and n = 4.
  • Step 5: We want the term where x has an exponent of 1, which means we need to find the term where (2x) is raised to the power of 1.
  • Step 6: This means we need to find the term where k = 3 (since n - k = 1).
  • Step 7: Calculate C(4, 3), which is the number of ways to choose 3 from 4. C(4, 3) = 4.
  • Step 8: Calculate (2)^1, which is 2.
  • Step 9: Calculate (3)^3, which is 27.
  • Step 10: Multiply these values together: 4 (from C(4, 3)) * 2 (from (2)^1) * 27 (from (3)^3).
  • Step 11: The final calculation is 4 * 2 * 27 = 216.
  • Binomial Expansion – The process of expanding expressions of the form (a + b)^n using the Binomial Theorem.
  • Coefficients in Binomial Expansion – Understanding how to find specific coefficients in the expansion using combinations and powers.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks