Pre-Algebra Demystified

PRACTICE

Add:

1. (6x^2 þ3x
   8)þ(2x^2
   5x
   9)


2. (3xþ2y
   2)þ(4x
   2yþ8)


3. (2xþ5)þ(7x
   10)þ(3x
   4)þ(4x
   6)


4. (3a^2 b^2
   2abþ5)þ(a^2 b^2 þ2abþ4)


5. (9mþ5n
   2)þ(4n
   8)þ(6mþ7)

ANSWERS

1. 8x^2
   2x
   17


2. 7xþ 6


3. 16x
   15


4. 4a^2 b^2 þ 9


5. 15mþ9n
   3

Subtraction of Polynomials

In Chapter 2 you learned that whenever you subtract integers in algebra, you
add the opposite. For example,
10
ð
6 Þ¼
10 þ 6 ¼
4. To find the
opposite of an integer (except 0), we change its sign. To find the opposite of a
monomial, change the sign of the numerical coefficient: e.g., the opposite of

7xy is 7xy and the opposite of 8x^2 is
8x^2.
To find the opposite of a polynomial, change the signs of every term of
the polynomial: e.g., the opposite of 6x^2
3xþ2is
(6x^2
3xþ2) or

6x^2 þ3x
2.

To subtract two polynomials, add the opposite of the polynomial being

subtracted.

EXAMPLE
Subtract (9x^2 þ3x
2)
(6x^2 þ5x
8).

SOLUTION

ð9x^2 þ3x
 2 Þ
ð6x^2 þ5x
 8 Þ¼9x^2 þ3x
 2 
6x^2 
5xþ 8

¼ð9x^2 
6x^2 Þþð3x
5xÞþð
 2 þ 8 Þ

¼3x^2 þð
2xÞþ 6

¼3x^2 
2xþ 6

CHAPTER 12 Monomials and Polynomials 235