Podcast
Questions and Answers
Find the coefficient of the 4th term in the expansion of (x + 3)^8.
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.
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.
Find the 2nd term in the expansion of (x + 5)^7.
35x^6
Use the Binomial Theorem to expand (2x + 3)^4.
Use the Binomial Theorem to expand (2x + 3)^4.
Signup and view all the answers
Use the Binomial Theorem to expand (3x + 1)^6.
Use the Binomial Theorem to expand (3x + 1)^6.
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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!
