Page 730 - Basic College Mathematics with Early Integers

706 A PPEND I X B I EXPONENTS AND POLYNOMIALS

PRACTICE 4 Example 4 Find the sum of 1-y + 2y + 1.72 and 112y - 6y - 3.62. Use a
2
2
Add the polynomials in vertical format.
Practice 3 vertically. Solution: Line up like terms underneath one another.
2
-y + 2y + 1.7
2
+12y - 6y - 3.6
2
11y - 4y - 1.9
Work Practice 4

Notice that we are finding the same sum in Example 4 as in Example 3. Of
course, the results are the same.

Objective Subtracting Polynomials

To subtract one polynomial from another, recall how we subtract numbers. To sub-
tract a number, we add its opposite: a - b = a + 1-b2.
For example,

7 - 10 = 7 + 1-102
=-3

To subtract a polynomial, we also add its opposite. Just as the opposite of 3 is -3,
2 2
the opposite of 12x - 5x + 12 is -12x - 5x + 12. Let’s practice simplifying the
opposite of a polynomial.

2
PRACTICE 5 Example 5 Simplify: -12x - 5x + 12
2
Simplify: -17y + 4y - 62
2
2
Solution: Rewrite -12x - 5x + 12 as -112x - 5x + 12 and use the
distributive property.
2
2
–(2x -5x+1)=–1(2x -5x+1)
2
=–1(2x )+(–1)(–5x)+(–1)(1)
2
=–2x +5x-1
Work Practice 5
Notice the result of Example 5.
2
2
-12x - 5x + 12 =-2x + 5x - 1
This means that the opposite of a polynomial can be found by changing the signs of
the terms of the polynomial. This leads to the following.

Subtracting Polynomials
To subtract polynomials, change the signs of the terms of the polynomial being
subtracted, then add.

PRACTICE 6 Example 6 Subtract: 15a + 72 - 12a - 102

Subtract:
13b - 22 - 17b + 232 Solution:
15a + 72 - 12a - 102 = 15a + 72 + 1-2a + 102 Add the opposite of 2a - 10.
= 5a - 2a + 7 + 10 Group like terms. Copyright 2012 Pearson Education, Inc.
Answers
2
4. -2z - 6.1z + 15 = 3a + 17
2
5. -7y - 4y + 6 Work Practice 6
6. -4b - 25