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Unit 3.5
SWBAT:
• Combine like terms
• Use the distributive property
Agenda
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Agenda
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Remember past vocab: Term
Term: a number, variable, or the product
(multiplication) of a number and a variable.
4 + 3y + 2 – 7
TERMS are separated by operation symbols
New Vocabulary: Like Terms
Terms that have exactly the same variable factors
(Exactly the same variables multiplied by a number)
Like Terms:
Not Like Terms:
-5 and 8
-5x and 8
2x and -3x
2x2 and -3x
2xy and -3xy
2x and -3xy
Identify the like terms
Which ones are like terms with 4xy?
1) -5xy
2) 3x
3) (3/5)xy
4) 7020234xy2
5) 52
6) 809xyz
Identify the like terms
Which ones are like terms with 4xy?
1) -5xy
2) 3x
THIS ONE
3) (3/5)xy
4) 7020234xy2
THIS ONE
5) 52
6) 809xyz
Quick Answer!
First table team to have everyone raise their hands gets
a sticker!
Which letter(s) are similar terms with 16xy?
A) 14x
B) 5y
C) 16xy2
D) 4xy
Quick Answer!
First table team to have everyone raise their hands gets
a sticker!
Which letter(s) are similar terms with 16xy?
A) 14x
B) 5y
C) 16xy2
D) 4xy
Like terms can be simplified
Simplifying happens only on ONE SIDE of an
equation or expression.
Only like terms can be simplified.
Side Note: Variables w/out
numbers
Remember: variables without numbers in front of
them are the same as a variable being multiplied by 1.
X = 1x
-Y = -1Y
Combining like terms
Combining like terms: On the SAME side of an
equation you will add/subtract them together, based
on what their signs say. You’re just re-organizing.
Ex. 5y + 4y – 2y = 2
(5 + 4 – 2)y = 2
7y = 2
Combining like terms:
Example 1
Combine like terms in 5m + 9m + m
= (5 + 9 + 1)m
= 15m
Combining like terms:
Example 2
Simplify 6p + 4y + 8 – 4p + 3
(6 – 4)p + 4y + (8 + 3)
2p + 4y + 11
You Try
Simplify 6x + 7y + 3x
You Try: ANSWERS
= 6x + 7y + 3x
= (6 + 3)x + 7y
= 9x + 7y
Now Try:
1) 7x + 5y + 6y + 3
4) 7y – 3p + 17x – 1
2) 4x + 10p – 15 + 6
5) 28p – 12p + 11 – 15
3) 8y – 3p + 12 - 1
6) 3p + 12r + 6p - 10
Now Try:
1) 7x + 5y + 6y + 3
7x + 11y + 3
2) 4x + 10p – 15 + 6
4x + 10p - 9
3) 8y – 3p + 12 – 1
8y – 3p + 11
4) 7y – 3p + 17x – 1
7y – 3p + 17x - 1
5) 28p – 12p + 11 – 15
16p - 4
6) 3p + 12r + 6p – 10
9p + 12r - 10
Word Problems!!!!
YAAAAAYYYYYYY!!!!!
Robert buys 5 loaves of bread and 8 cans of tuna for a
picnic. Melissa buys a loaf of bread and 2 cans of tuna.
Define and use variables to represent the total cost.
B = cost of a loaf of bread
T = cost of a can of tuna
Robert: 5b + 8t
Melissa: 2t + 1b
5b + 8t + 2t + 1b
= 6b + 10t
You try:
In one trip to a hardware store, you buy 16 boards, 2
boxes of nails, and a hammer. On a second trip, you
buy 10 more boards and a box of nails. Define and use
variables to represent the total cost.
You try:
In one trip to a hardware store, you buy 16 boards, 2 boxes
of nails, and a hammer. On a second trip, you buy 10 more
boards and a box of nails. Define and use variables to
represent the total cost.
b = cost of board
n = cost of nails
h = cost of a hammer
16b + 2n + h + 10b + n
=26b + 3n + h
Now Try: Write the expression for
the following situations
1) Alexis buys a beach
house, 2 dogs and a pet
cat one day, and a second
beach house, 4 more dogs,
and another pet cat the
next day.
2) Tyreek runs for 12
miles, then hikes for 19
upwards, continues to run
4 miles, then hikes
upwards 6 miles.
3) Bryena eats 14 candy
bars, then 3 bags of chips,
then another 8 candy bars
before eating a whole
cake.
4) Cye-Enn colors for 8
minutes, then dances for
15 minutes, colors for
another 12 minutes, then
eats for 12.
Now Try: Write the expression for
the following situations
1) 2b + 6d + 2c
3) 22b + 3h + c
(where b = candy bars,
h=chips, c = cake)
2) 16r + 25h
4) 20c + 15d + 12e
Distributive Property
Distributive property: a (b + c) = ab + ac
You’re multiplying the number outside the parenthesis by
both of the numbers inside the parenthesis, but keeping the
same sign.
Ex)
5 (4t – 3)
= 5(4t) – 5(3)
= 20t - 15
Distributive property slow-mo
Simplify:
3( x - 2 )
3x
- 3(2)
3x
- 6
Distributive Property Simplifying:
Example
Simplify 5(t + 3) + 8t
5t + 15 + 8t
(5 + 8)t + 15
13t + 15
You Try
Simplify 6t – 14 + 3(t – 2)
You Try: ANSWERS
Simplify 6t – 14 + 3(t – 2)
6t – 14 + 3t – 6
(6 + 3)t + (-14 – 6)
9t + -20
Now Try
1) 8c – 3(c + 5)
4) 3x – 11 + 3(4-x)
2) 8d + 6(4 – d)
5) 2x + 2(-3x – 11)
3) 4x – 12 + 5(d + 2)
6) -5(c + 3) - 13
Now Try
1) 8c – 3(c + 5)
5c - 15
2) 8d + 6(4 – d)
2d + 24
3) 4x – 12 + 5(d + 2)
4x + 5d - 2
4) 3x – 11 + 3(4 - x)
15x - 11
5) 2x + 2(-3x – 11)
-4x - 22
6) -5(c + 3) – 13
-5c -28