8.2 Simplifying Algebraic Expressions 655Self Check 9
Simplify:
Now TryProblem 937 y^2 21 y 2 y 6EXAMPLE (^9) Simplify:
StrategyFirst, we will identify any like terms in the expression. Then we will use
the distributive property in reverse to combine them.
WHYTo simplifyan expression we use properties of real numbers to write an
equivalent expression in simpler form.
Solution
We can combine the like terms that involve the variable.
6 a^2 54 a 4 a 36 6 a^2 50 a 36 Think: .(544)a 50 a
a
6 a^2 54 a 4 a 36
EXAMPLE (^10) Simplify:
StrategyFirst, we will remove the parentheses. Then we will identify any like
terms and combine them.
WHYTo simplifyan expression we use properties of real numbers, such as the
distributive property, to write an equivalent expression in simpler form.
Solution
Here, the distributive property is used both forward(to remove parentheses) and
in reverse(to combine like terms).
Think:.
Think: .(20 5 4) 19
2 x 19 (42)x^2 x
Distribute the multiplication
4 x 20 5 2 x (^4) by 4 and 1.
Replace the symbol
in front of (2x4)
with 1.
4(x5) 5 (2x4)4(x5) 5 1 (2x4)
4(x5) 5 (2x4)
Self Check 10
Simplify:
Now TryProblem 99
6(3y1) 2 ( 3 y4)
- a. b. c. d. 2. a. b. c.
- a. b. c. 4. a. b.
c. 5. 6. a. and b. and ; and 2 - a. b. c. d.does not simplify e. 8. a. b. c.
d.h 9. 7 y^2 19 y 6 10. 21 y 8
8 x 3 y 0.5s^476 c 8 h 10 h h1.4r3.5s5.6 5 x 18 2 y 7 y 5 p^217 p^2 1210 x 5 9 y 36 c 22 2 x 8 54 c 108 d54 s 48 u m 8 y 7 m 14 640 x 240 4 y 9ANSWERS TO SELF CHECKSFill in the blanks.
1.To the expression means to write it in
simpler form:.
- and are expressions because for
each value of , they represent the same number.
3.To perform the multiplication , we use the
(^) property.
2(x8)
x
5(6x) 30 x^
5(6x) 30 x
(^) 5(6x)
VOCABULARY 4.We call the of a sum.
5.Terms such as and , which have the same
variables raised to exactly the same power, are called
terms.
6.When we write as , we say we have
(^) like terms.
9 xx 10 x
7 x^25 x^2
(c9)^
SECTION 8.2 STUDY SET