Page 741 - Basic College Mathematics with Early Integers

B.3 MULTIPLYING POLYNOMIALS Objectives

Multiply a Monomial and Any
Polynomial.
Objective Multiplying a Monomial and a Polynomial
Multiply Two Binomials.
Recall that a polynomial that consists of one term is called a monomial. For exam-
ple, 5x is a monomial. To multiply a monomial and any polynomial, we use the dis- Square a Binomial.
tributive property
Use the FOIL Order to Multiply
a1b + c2 = a b + a c
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#
Binomials.
and apply properties of exponents.
Multiply Any Two Polynomials.
Example 1 Multiply: 5x13x + 22 PRACTICE 1
2
2
Multiply: 3y17y + 52
Solution:
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2
2
5x(3x +2)=5x 3x +5x 2 Apply the distributive property.
3
=15x +10x
Work Practice 1
Example 2 Multiply: 2z14z + 6z - 92 PRACTICE 2
2
2
Multiply: 5r18r - r + 112
Solution:
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2
2
2z(4z +6z-9)=2z 4z +2z 6z+2z(–9)
3
2
=8z +12z -18z
Work Practice 2
To visualize multiplication by a monomial, let’s look at two ways we can repre-
sent the area of the same rectangle.
The width of the rectangle is x and its length is x + 3. One way to calculate the
area of the rectangle is
x 3

x

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area = width length
= x1x + 32
Another way to calculate the area of the rectangle is to find the sum of the areas of
the smaller figures.
x 3

area: area:
x
x 2 3x

area = x + 3x
2
Since the areas must be equal, we have that
Answers
x1x + 32 = x + 3x As expected by the distributive property 1. 21y + 15y 2. 40r - 5r + 55r
2
2
3
3
717