First Outer Inner Last

1
First Outer Inner Last
Write the following in the expanded form

• 1. (2x 3) (3x7)
• 2. (3y 4) (4y 5)
• 3. (2m 5) (3m 1)
• (2a 1) (3a - 1)
• 5. (4b 7) (2b 1)

2
First Outer Inner Last
First
Outer
Inner
Last
Example 1. (2x 3) (3x7)
6x2
(2x 3) (3x7)
(2x 3) (3x7)
14x
(2x 3) (3x7)
9x
(2x 3) (3x7)
21
3
First Outer Inner Last
Continues
6x2 14x 9x 21
6x2 23x 21
Answer
6x2 23x 21
4
Factoring binomials
There are 2 difference ways to do it

• 1. m2 9m 20
• 2. g2 4g 3
• 3. x2 x 12
• 4. a2 5a 24
• 5. m2 - 49

5
Factoring binomials
Continues
First one

• Example 1. m2 9m 20

20 4 5
20 2 10
(m 2 ) (m - 10)
First Trails
Checking
(m 2 ) (m - 10)
m2 12m 20
(m 4 ) (m - 5)
Second Trails
Checking
(m 4 ) (m - 5)
m2 9m 20
6
Continues
Factoring binomials
Second one

• Example 1. 3x2 6x - 72

216322233
12 18 -6
3x2 12x 18x - 72
3x( x 4) 18 ( x 4)
( x 4) (3x - 18)
7
Exploring Counting Problem
Talk it Over
Suppose you are packing for a trip and can take
only one small bag of clothes. How do you decide
what to pack? Suppose you decide to take three
shirts, a pair of jeans, and a pair of shorts,
all of which are color-coordinated. How can you
make a complete list of all the possible outfits
without counting any outfit more than once?
1. a.
b.
Suppose you are having posters for play printed
in two colors. Your color choices are
black, blue, red, green, and purple. How can you
make a complete list of all the possible pairs of
colors without counting any pair more than
once? How are the situations in questions 1(B)
and 2 alike?
How are they different?
2.
3.
You can organize information in a systematic way
so that you list all possibilities without
listing anything more than once.
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Sample 1
Suppose you go to a snack bar that has the menu
shown and buy a complete meal. How many
different meals are there a choose from?
MENU MAIN DESES 2.75 Tacos,
Burritos, Enchiladas SIDE DISHES .50 Rice, Pinto
Beans DRINKS .75 Lemonade, Spring Water COMPLETE
MEAL 3.50 Includes a main dish, a side dish, and
a drink
Sample Response..
Problem Solving Strategy Use a diagram
Make a tree diagram with a column of branches for
each category. To keep it simple, label each
branch in each category with a sing letter. Use a
different letter for each item.
Three main Dish choices
Two side Dish choices
Two drink Choices
Outcomes
L
TRL
Tacos, rice, lemonade
R
S
TRS
Tacos, rice, spring water
L
TPL
Tacos, pinto beans, lemonade
T
P
S
TPS
Tacos, pinto beans, spring water
L
BRL
burritos, rice, lemonade
S
BRS
burritos, rice, spring water
R
L
BPL
burritos, pinto beans, lemonade
B
S
BPS
burritos, pinto beans, spring water
P
L
enchiladas, rice, lemonade
ERL
S
Enchiladas, rice, spring water
ERS
R
L
enchiladas, pinto beans, lemonade
EPL
E
S
enchiladas, pinto beans, spring water
EPS
P
Each of the 12 different possibilities is an
outcome.