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Unit 3.5SWBAT:•Combine like terms•Use the distributive property

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5 minute chat break

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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

2) 4x + 10p – 15 + 6

3) 8y – 3p + 12 - 1

4) 7y – 3p + 17x – 1

5) 28p – 12p + 11 – 15

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

2) 16r + 25h

3) 22b + 3h + c

(where b = candy bars, h=chips, c = cake)

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)

• 2) 8d + 6(4 – d)

• 3) 4x – 12 + 5(d + 2)

• 4) 3x – 11 + 3(4-x)

• 5) 2x + 2(-3x – 11)

• 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