6.2.1: Multiply polynomials.

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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 Pascals 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.
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(x2 4x 1)(x2 5x 2)
Find the product.
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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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.
Pascals Triangle
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Each row of Pascals 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.
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Example 3 Using Pascals Triangle to Expand
Binomial Expressions
Expand each expression.
Identify the coefficients for n 3, or row 3.
A. (k 5)3
____(____)3(_____)0____(____)2(____)1____(_
___)1(____)2____(____)0(____)3
B. (6m 8)3