Binomial Expansion Worksheet

Binomial Expansion Worksheet

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. The coefficients of the binomial expansion \((a+b)^n\) can be found using  .

2. The Binomial Theorem states that for any positive integer \(n\), the expansion of \((x+y)^n\) is given by \(\sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k\), where \(\binom{n}{k}\) is the   coefficient.

3. Expand \((2x + 3y)^3\) using the binomial theorem.

4. What is the coefficient of the \(x^2y^3\) term in the expansion of \((x+y)^5\)?

5. Find the 4th term in the expansion of \((x - 2)^7\).

6. The sum of the exponents in each term of a binomial expansion \((a+b)^n\) is always equal to \(n\).

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