1. LEARNING GOALS – LESSON 6.2
6.2.1: Multiply polynomials.
6.2.2: Use binomial expansion to expand binomial expressions that
are raised to positive integer powers.
6.2.3: Use Pascal’s Triangle to expand binomial expressions.
Example 1A: Multiplying a Monomial and a Polynomial
Find each product.
A. 4y2(y2 + 3)
B. fg(f4 + 2f3g – 3f2g2 + fg3)
To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first.
Keep in mind that if one polynomial has m terms and the other has n terms, then the product has mn terms before it is simplified.
Example 1B: Multiplying Polynomials
Find the product.
(a – 3)(2 – 5a + a2)
Method 1 Multiply horizontally.
Method 2 Multiply vertically.

2. Example 1C: Business Application
Find the product.
(x2 – 4x + 1)(x2 + 5x – 2)
Example 1C: Business Application
A standard Burly Box is p ft by 3p ft by 4p ft. A large Burly Box has 1.5 ft added to each dimension. Write a polynomial V(p) in standard form that can be used to find the volume of a large Burly Box.
Example 2: Expanding a Power of a Binomial
A. Find the product.
(a + 2b)3
Write in expanded form.
Multiply the last two binomial factors.
Distribute a and then 2b.
Combine like terms.

3. Pascal’s Triangle B. Find the product. (2x – 1)3
Write in expanded form.
Multiply the last two binomial factors.
Distribute 2x and then –1.
Combine like terms.
Pascal’s Triangle

4. Each row of Pascal’s triangle gives the coefficients of the corresponding binomial expansion. The pattern in the table can be extended to apply to the expansion of any binomial of the form (a + b)n, where n is a whole number.

5. Example 3: Using Pascal’s Triangle to Expand Binomial Expressions
Expand each expression.
A. (k – 5)3
Identify the coefficients for n = 3, or row 3.
[____(____)3(_____)0]+[____(____)2(____)1]+[____(____)1(____)2]+[____(____)0(____)3]
B. (6m – 8)3