Binomial Expansion Worksheet

Binomial Expansion

Read each question carefully and show all your work. Use Pascal's Triangle or the Binomial Theorem to expand the given expressions.

Pascal's Triangle is a triangular array of the binomial coefficients. Each number is the sum of the two numbers directly above it.

Fill in the missing numbers in Pascal's Triangle below:

Row 0: 1

Row 1: 1 1

Row 2: 1 2 1

Row 3: 1 3 3 1

Row 4: 1 _ _ _ 1

Row 5: 1 _ _ _ _ 1

1. The coefficients in the expansion of (a + b)ⁿ are given by the   triangle.

2. The binomial theorem provides a formula for expanding any power of a  .

3. The sum of the exponents of a and b in each term of a binomial expansion is always equal to  .

1. Expand (x + y)³ using Pascal's Triangle.

2. Expand (2a - b)⁴ using the binomial theorem.

1. What is the coefficient of the x²y³ term in the expansion of (x + y)⁵?

1. Find the 3rd term in the expansion of (3x - 2y)⁶.