Algebra 2 Binomial Theorem Quiz

Questions and Answers

Find the coefficient of the 4th term in the expansion of (x + 3)^8.

1512

Find the coefficient of the 6th term in the expansion of (x + 2)^11.

14784

Find the 2nd term in the expansion of (x + 5)^7.

35x^6

Use the Binomial Theorem to expand (2x + 3)^4.

<p>16x^4 + 96x^3 + 216x^2 + 216x + 81</p> Signup and view all the answers

Use the Binomial Theorem to expand (3x + 1)^6.

<p>729x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1</p> Signup and view all the answers

Study Notes

Binomial Theorem Key Concepts

The Binomial Theorem allows for the expansion of expressions in the form of (a + b)^n, where coefficients can be determined using combinations.
Each term in the expansion can be represented as C(n, k)a^(n-k)b^k, where C(n, k) is the binomial coefficient.

Example Problems

4th Term Coefficient of (x + 3)^8
- Coefficient calculated: 1512
- Term structure follows the binomial expansion rules.
6th Term Coefficient of (x + 2)^11
- Coefficient determined: 14784
- Utilizes the formula for a specific term in the expansion.
2nd Term of (x + 5)^7
- Result is 35x^6
- The second term is calculated using binomial expansion principles.

Expansions Using Binomial Theorem

Expansion of (2x + 3)^4
- Resulting expression: 16x^4 + 96x^3 + 216x^2 + 216x + 81
- Each term arises from applying the binomial theorem correctly to the coefficients and powers.
Expansion of (3x + 1)^6
- Resulting expression: 729x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1
- Each term includes the corresponding coefficient and powers of x as per binomial expansion.

Description

Test your knowledge of the Binomial Theorem with this engaging Algebra 2 quiz. Each question focuses on finding coefficients and terms in binomial expansions. Perfect for reinforcing concepts and preparing for exams!