6-2
Multiplying Polynomials
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
Keep in mind that if
two polynomials,
one polynomial has
use the
m terms and the
Distributive
other has n terms,
Property and
then the product has
multiply each
mn terms before it is
term in the
simplified.
second
polynomial by
each term in the
first.
Example 1B: Multiplying Polynomials
Find the product.
(a – 3)(2 – 5a + a2)
Method 1 Multiply horizontally.
Method 2 Multiply vertically.
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Multiplying Polynomials
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.
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Multiplying Polynomials
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
6-2
Multiplying Polynomials
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.
(a  b )6
6-2
Multiplying Polynomials
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