### - - Reteaching with Practice

```Date
_
- - Reteaching with Practice
~
For use with pages 16-23
(Slim
Simplify algebraic expressions.
Vocabulary
In an expression that can be written as a sum, the parts added together
are called the terms.
When a term is a product of a number and a power of a variable, the
number is called the coefficient of the power.
Like terms have the same variable parts.
If a term has a number part but no variable part, it is called
a constant term.
An expression in which all grouping symbols are removed and all like
terms are combined is a simplified expression.
Jf£tMIQ!11 Identify coefficients and like terms
Identify theccefflclents and like terms in the expression
2x - 4Xl + 5 - 7 Xl - 3 + 9x.
Solution
Begin by writing the expression as a sum in order to identify the terms.
+ 9x = 2x + (-4x 2) + 5 + (-7x 2) + (-3) + 9x
2x - 4x 2 + 5 - 7x 2 - 3
:>­
co
CtJ
0..
The coefficients ofthe expression are 2, -4, -7, and 9. The terms 2x and
9x are like terms. The terms -4x2 and -7x2 are also like terms. The terms
Q_ ""...'1- ..... Cf 1-
5 and - 3 are also like terms.
Exercises for Example 1
.
.-
,rl? Loe.f-f:
.--/
1.
~-7-3x2+~.~/
3.
- 3t
+ 8t 2 + 8t + 9 + 4t 2
C~<.;..i;.'i,+../ : - 3"'-'b" b L:=-
~u
. .' I { I
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~)
E
a
U
7 (£,; r"-p ,; t=i eel)
co
- 3/ LI
.8
LoeAr . ..
<'&'1 II - '3>, ...;6y2 + 7y - 8 - 3y2 + 5y
,"=.
---==-
4. l2w - 5w + 3 +
+ 3w - 7
2.
8w
I
.c
Q)
::>
a
::r::
'+­
a
co
a
'iii
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-0
CtJ
Simplify by combining like terms
-6(y - 2)
co
+ 4(y - 1) = -6y + 12 + 4y - 4
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t:'
Distributive property
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= (-6y + 4y) +
(12 - 4)
= -2y + 8
a
Group like terms.
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Combine like terms.
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x:
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Exercises for Example 2
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a
U
Simplify by combining like terms.
5.
3t
+ 5t 2 - 2t + 6t 2
7. -4(m - 2) + 3(m + 1)
_ Ltm t- e t- 3 tl'/ r 3
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32
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Algebra 2 Concepts and Skills
Chapter 1 Resource Book
..-----------­ + 5q + 14
6.
7(q - 2)
8.
2
2)
8d, + 2d ~ 3(d +. d _ J.2­
8"c-l. t 2tt - 3d - :-SC\
C=d-Z;5~ll
Date
Reteaching with Practice
~~~--'
_
~
continued
Foruse with pages 16-23
Imm!1:1
Simplify expressions with grouping symbols
Simplify the expression 2x
+
5(3x ­ 7).
Solution
2x
+ 5(3x - 7)
= 2x
= (2x
+ 15x ­ 35
+
Distributive property
15x) ­ 35
Group like terms.
= 17x ­ 35
Combine like terms.
(j)30'1 - uc + ~ 'I
?> 3'y- Lto
r.,»
...,,' -.-r--"
~ <,'7, c> ""
~j ~Hl
r: '1
Exercises for Example 3
Simplify the expression. ,
9.
+ 3y
5(6y - 8)
r •
.-
10.
11.4(-5n-7)+3(3n-9)
12.
7h - 2(5h
,
5
+ 4)
-6(4d-2)-4(2d+8)
-'v,--td
iImiI~!1:1
- , --, =-1/r1- 5
I
Simplify a mathematical model
'-"5'd -3..:J.
-3 ..L d '-2_0
t /2.
The width of a rectangular patio is n + 3 and the length of the patio is
7 n. Write and simplify an expression that represents the perimeter of
the patio. Then find the perimeter if n = 2 feet.
Solution
Write a verbal model. Then write an algebraic expression.
Number
of sides
Width
(in feet)
~
~
(n
2
'0
c;
a
'0
~
+
7n
2
An algebraic expression for the perimeter is P = 2(n
'(;;
:~
+ 3)
2(n
+ 3) + 2(7n)
=
2n
=
(2n
co
=
When n
+ 6 + 14n
+ 14n) + 6
16n + 6
Group like terms.
Combine like terms.
= 2, the perimeter is 16(2) + 6 = 32 + 6 = 38 feet.
@
13.
.
eo::
e :::
_
2-(
J. ( ;l. n -\" 3/ -+­
5 n)
I-b', +- {; + \0 ~I -t/' 1,"* Y1 -t-(:,
The width of a rectangular patio is 2n + 3 and the length of the patio is 5n. Write
and simplify an expression that represents the perimeter ofthe patio. Then find
the perimeter if n = 4 feet.
t..\- (y--') ;-6
&. 2­ ~: eCi"
r:;. \
14.
+ 3) + 2(7n).
Distributive property
Exercises for Example 4
)
Length
(in feet)
Number
of sides
+
e .:
You purchase 12 packages of wrapping paper. Large packages cost \$7 and small
packages cost,\$4.50. Write and simplify an expression that represents the total
cost if n of the 12 packages are large packages. Then find the total cost if 8 of the
12yackages ar~~arge packa~~s.
~ 1'S (f;)
S'-\- ::\$.
~
In
v/ n
+
t-
4. S ( (2-- ­ tI )
-I-
SLf - Y
~ iSh
I
~. n
+-'51f
'7tf
Algebra 2 Concepts and Skills
Chapter 1Resource Book
33
Name
_
Date
_
_ _ Practice A
~
Foruse with pages 16-23
Identify the terms in the expression.
1.
3w - 10
3.
- 9n
+
14 - 3n2
+9
2.
8d 2
4.
8 + 7r - 9,-2
-
3d
Identify the coefficients and like terms in the expression.
5.
Y+
7.
l5t - lOt2 + 6t - 9 + 2f2
6 - 5y + lOy
6.
-6x + 7x 2
8.
4m + 7 - 8m - 9
-
5 + 8x
Simplify the expression by combining like terms.
-4n + 9n
10.
8x - lOx
11.
-9m + 3 + 7m
12.
17d - lId - 8
13.
12 - 9z + 6
14.
15 - 8p - 9 + 2p
15.
-9y + lOy 2 + 5y + 2y 2
16.
8n2 + 7n - 9n2
9.
+ 9b2
17. b' - b
-
-
l8n
7b
Simplify the expression.
18.
-3(v-2)+5v
19.
8 + 5([ + 4)
20.
-(q + 6) + 4q
21.
2(6t - 9) + 5(2t+ 1)
23.
5(2c - 1) - 8c
22. -7(2h - 4)
24. 7(3w 2
26.
-
+ 6(3h - 8)
4w) - 5(w2
-
w)
>­
c::
co
a.
E
o
co
25. 5(,-2 + r) - 3(,-2 - 2r)
,0=
~
~
c::
5 - 2(2.5a + 7)
.8
..c:
27.
Cl
::::l
Tips You work with 6 other people at an ice cream stand. At the end of the night,
o
:r:
you divide the tips evenly. Write an expression to show how much each person
receives. If the tips equal \$110.70, how much does each person get?
'+­
o
c;
,,=,
tn
:~
28.
'0
Tickets You and some friends are going to a concert. Tickets cost \$20 each. There
is a \$4 charge to order the tickets online. Write an expression for the total cost of
ordering the tickets online. Then find the total cost if you order 7 tickets.
co
Q)
to
:.::::;
co
Cl
::::l
29.
o
Bike Rental You are renting a bike. It costs \$5 for a helmet and \$3 per hour. Write
o
an expression for the total cost of renting a bike. Find the total cost if you plan to
use the bike for 4 hours.
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~
9
+-'
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Cl
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a.
o
co
l
30
Algebra 2 Concepts and Skills
Chapter 1 Resource Book
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