Binomial Theorem Mastery: Grade 12

Binomial Theorem Mastery

Read each question carefully and provide clear, detailed solutions. Show all your work for full credit. You may use a calculator for calculations, but all steps for binomial expansion must be shown.

1. Expand the following binomial expression using the Binomial Theorem:

$(2x + 3y)^4$

2. For the expansion of $(x - 2)^5$, the coefficient of the $x^3$ term is  .

3. The third term in the expansion of $(a + b)^6$ is  .

4. The number of terms in the expansion of $(a+b)^n$ is $n$.

5. The sum of the exponents in each term of a binomial expansion $(a+b)^n$ is always $n$.

6. What is the coefficient of $x^2y^3$ in the expansion of $(x + y)^5$?

7. Which of the following is the general term in the expansion of $(a+b)^n$?

8. Find the term independent of $x$ in the expansion of $(x^2 + \frac{1}{x})^{9}$.