NAME
DATE
PERIOD __
Study Guide
Student Edition
Pages 388-393
Adding and Subtracting Polynomials
To add polynomials, group the like terms together and then find
the sum. 3x2 and x2 are like terms. x2 and x, and x2 and y2 are
unlike terms.
Example 1: Find (3x2 + 2x - 5) + (x2 + 4x + 4).
(3x2 + 2x - 5) + (x2 + 4x + 4)
= (3x2 + 2x + (-5)) + (x2 + 4x + 4)
= (3x2 + x2) + (2x + 4x) + (- 5 + 4)
= (3 + l)x2 + (2 + 4)x + (-5 + 4)
= 4X2 + 6x - 1
Rewrite subtraction.
Regroup like terms.
Distributive property
Simplify.
You can subtract a polynomial by adding its additive inverse.
Example 2: Find the additive inverse of 5b2 - 3.
The additive inverse is -(5b2 - 3) or -5b2 + 3.
Example 3: Find (4m3
(4m3
=
=
=
=
-
6) - (7m3
-
9).
6) - (7m3 - 9)
(4m3 - 6) + (-7m3 + 9) The additive inverse of 7m3
(4m3 - 7m3) + (-6 + 9) Regroup like terms.
(4 - 7)m3 + (-6 + 9)
Distributive property
3
Simplify.
-3m
+ 3
-
-
9 is -7m3
+ 9.
Find each sum or difference.
2. (8w2
1. (2a + 3) + (5a + 1)
3. (-5c4
+ 2c2 - 6) + (6c4
5. (4g + h3) + (-9g
-
2c2 + 5)
+ s) - (6s2 - 8s)
13. (7y2 + 2y + 21) - (9y2 + 6y + 11)
© Glencoe/McGraw-Hili
+
(7w2 - 3w)
6. (2 - 16x2) + (8 - 16x2)
8. (35a2 + 15a - 20) + (10a2 + 25)
7. (18 + 5xy) + (-6 - 10xy)
11. (-18s2
w)
4. (12m - 5n) + (12m + 5n)
- 4h3)
9. (6d + 3) - (4d + 5)
+
10. (14 - 3t) - (2 + 7t)
12. (26g - 13gh) - (- 2g
14. (-5m2
56
+ gh)
+ 2n - 1) - (7m2 + 16n - 8)
Algebra: Concepts and Applications