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FUNDAMENTALS DISCIPLINE

BLACK BELT TRAINING

COMBINING

NAME_______________________________

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Black Belt Order of Mastery

1. Combining neg/pos integers

2. Order of operations

3. Evaluating expressions

4. Distributive property

5. Combining like terms

Congratulations, Grasshopper! You are now ready to learn the foundational skills

necessary to tackle Algebra. These are the Fundamentals….that is, these are the

skills that you will use for the rest of your mathematical career. You will use these

skills in Algebra and all the way through Calculus. So, be prepared….be

ready….become a Master of the Fundamentals.

No Doubt! There are a lot of problems in this packet….but its important! Wax On,

Wax Off Grasshopper….Now, go get your Black Belt

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NEGATIVE AND POSITIVE INTEGERS I like to think of negative and positive integers as actual things, like French fries!

For instance, have you ever gone to McDonald’s and ordered fries? Most of them are

delicious. But sometimes you get a burnt fry that tastes awful. They’re bad. Once

you eat a bad fry, the best way to get rid of that taste is to eat a good fry. So in other

words, one good fry cancels out one bad fry. That’s how I like to look at negatives

and positives. I look at negatives and call them BAD FRIES. I look at positives and

call them GOOD FRIES.

Example: -4 = 4 bad fries 3 = 3 good fries -2 = 2 bad fries 7 = 7 good fries

If you look at negatives and positives this way it makes it a lot easier to add ‘em up.

If you combine 1 bad fry with 1 good fry, they cancel out: -1 + 1 = 0

So when I’m dealing with integers I’m just trying to find out what I have more of,

good fries or bad fries. Whichever one I have more of, that’s what I’ll be left with.

Example: -7 + 3 = ?

Here I’ve got 7 bad fries and 3 good fries. That means I have 4 more bad fries than

good. So I end up with 4 bad fries = -4

If fries aren’t your thing, you could just call them positives and negatives if you want.

Example: -4 + 6 is like saying 4 negatives and 6 positives. +

+

So draw 4 negatives on your paper, then draw 6 positives. +

+

Each + cancels out one +

So if you cross off each pair, what are you left with? +

Whatever it is, that’s your answer! -4 + 6 = 2

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Of course there’s a more traditional way to look at it as well:

ADDITION:

If the signs are the same then you add the two numbers and keep the sign.

Ex. 6 + 2 = 8 or -6 + -2 = -8

If the signs are different, subtract the two numbers and take the sign of the larger number.

Ex. -6 + 2 = -4 or 6 + -2 = 4

SUBTRACTION:

Change the sign of the second number, then add the two numbers using the rules for addition, above.

Ex. 6 - 2 = 6 + (-2) = 4 Ex. -6 - -2 = -6 + (+2) = -4 Ex. -6 - 2 = -6 + (-2) = -8 Ex. 6 - -2 = 6 + (+2) = 8

MULTIPLICATION AND DIVISION:

Do the multiplication or division of the two numbers and then determine the sign by the following: If the

signs of the two numbers are the same the answer is positive.

Ex. 6*2 = 12 or -6*-2 = 12 Ex. 6/2 = 3 or -6/-2 = 3

If the signs of the two numbers are different the answer is negative.

Ex. -6*2 = -12 or 6*-2 = -12 Ex. -6/2 = -3 or 6/-2 = -3

When you're working with squaring and cubing negative numbers, just remember that squaring and cubing is like multiplying. For example,

22

= 2*2

34

= 3*3*3*3

So (-3)2

= (-3)*(-3)

Now just use the rules of multiplying two negative numbers together to get the answer. If

you're cubing a number, it's just as if you've multiplied it together three times.

Ex. (-4)3

= (-4)*(-4)*(-4)

Using the rules of multiplication, multiply the first two together to get 16. Then the problem becomes:

(16)*(-4)

and you can use the regular multiplication rules again.

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ADDING POSITIVE AND NEGATIVE INTEGERS Evaluate each expression.

1) 5 + −4 − 7 2) −2 − −2 − 4

3) −6 + 2 − −1 4) 6 − −4 − −4

5) −4 − −2 − −4 6) 6 − 6 + 5

7) 4 + 7 − −8 8) −3 + 6 − −4

9) 5 + 7 − 2 10) −1 − −1 + 1

Multipying Positive and Negative Integers Find each product.

11) −9 × −6 12) −8 × −3

13) 5 × −3 14) 9 × −2

15) −5 × −7 16) −10 × −9

17) 2 × −3 18) −3 × 2

19) −10 × 3 20) −3 × −9

21) −3 × −2 × −3 22) −2 × −5 × 5

23) −6 × −1 × −2 24) 4 × −2 × −4

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The Positive & Negative Number Connection

By now, you have worked with integers in some form or another. An Integer is just a Positive or Negative whole

number. Whether you are working with whole numbers or fractions, you must be able to Add/Subtract and

Multiply/Divide numbers that are Positive & Negative. Check out the basic rules…(note- these rules apply to when you

are using only two numbers)

Addition/Subtraction Rules:

1. Same Sign?? Then, you ADD the Numbers & Keep the sign 2. Different Signs?? Then, you SUBTRACT the Numbers & Keep sign of larger number.

Multiplication/Division Rules:

1. Same Sign??? Then, multiply or divide & answer is POSITIVE 2. Different Sign?? Then, multiply or divide & answer is NEGATIVE

Try these…..Add & Subtract

1. -20 + 10 2. -36 + 42 3. -44 + 37 4. -7 - 10

5. 3 – 7 – 8 6. (-5) – 4 + (-3) 7. 26 – 97 + 52

8. -125 + 50 – 10 9. 84 + (-50) – 78 + (-25) 10. -61 + 43 + (-30) + 35

Try These…..Multiply & Divide

11. 30 5 12. 70 14 13. 16 8 14. 5 19

15. 180 12 16. 98 14 17. 9(3)(8) 18. ( 6)(5)( 8)

19. 8( 2)(7)(3) 20. 110 10 21. 36

4 22.

285

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23. 10( 3)(8)( 5) 24. ( 10)(7)(2)

( 5)(2)( 3) 25.

(25)(8)( 3)

(4)( 5)( 6)

26. ( 144)( 6)(7)

( 7)(12) 27.

(7)( 32)(14)

( 2)(8)( 7) 28. 3( 4)(10)( 5)(11)( 2)

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Just look at these problems and determine whether answer will be Positive or Negative:

29. ( 19)(4)( 20)(3)( 8) 30. 4( 17)( 5)

( 1)(3( 18)

31. How did you determine your answer for the above problems? Can you make a rule?

Let’s make sure we keep our Fraction Skills up to date. Remember, to flip the second fraction when dividing. Try these…

32. (21

5)(5

7) 33. ( 1

1

4)( 2

7

8)

34. (5

7)(6

7) 35. (

2

5)(7

5) 36. ( 1

1

10)(22

3)

37.

2

73

38.

2

3

32

3

39. 32

79

7

40. 41

64

5

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What’s the Order?

Order of Operations You have done and heard this before. What is it? It is the Order in which you should do mathematical operations when

solving a long mathematical expression. The Order of Operations is NOT a topic. It’s the way you calculate all of math in

every topic no matter what math you’re doing. You always do it in this order.

To find the value of an expression, you must follow this order

1st- solve what’s inside the parenthesis.

2nd

– solve the exponents

3rd- multiply and divide (from left to right)

4th

– add and subtract (from left to right)

So you’ll need to broaden your vocabulary. A couple terms you need to know:

Expression- a mathematical phrase made up of a variable or a combination of variables

and/or numbers and operations.

Example: 23

+ (5-3)

Variable- a letter used to stand for a number in an expression or equation

The Order is: P E M or D A or S

Parentheses, Exponents, Multiplication Or Division, Addition or Subtraction

Always work Left to Right.

Follow the order PEMDAS

Do Multiplication or Division whichever comes first when working Left to Right

Do Addition or Subtraction whichever comes first when working Left to Right

When you use PEMDAS, you are just following an ordered system to SIMPLIFY a crazy math problem…that is, making it

smaller. A little bit crazy, but with practice you’ll get it down!

EXAMPLE: 62 – 4 (3 + 2) Do parentheses first

62

– 4 (5) Now you do the exponents

36 – 4 (5) Next is multiply

36 – 20 Finally subtract

16 You answer (the value of the expression)

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Now you give it a shot! Don’t forget the Order! It helps to WRITE OUT EACH STEP like I did in the example. Use another

sheet of paper and put each step below the next one so it’s easier to check if you made a mistake.

1. 10 (3 2) 9 2. 16 8 22 3. 6 3 2 7

4. 2 32 7 5. 7 (18 6) 6 6. (7 4)2 3 15

7. 10 (52 2) 6 8. 9 2

4 32 1 9.

53 2

1 62 8

10. 2(8 4)2 4 2 11. 6(4 2)2 6 4

12. (2 12 4 2) 8 2 13. 64 18 9( 4) 2 20

14. 12 4 2

8 4 6 15. 24 (8 4) 9 6

16. (30 6) 6(30) 3 17. (8 /2)3 (1 1)

18. Which is Correct? Explain Why.

(9 7)2 3

5(9 7)2 3 5

or

(9 7)2 3

5(9 7)2 3 5

Challenge (Percent Review)-

You decide to buy two rings from an outdoor vendor. One ring costs $10.89. The other ring costs $12.48. The sales tax

is 8%. The vendor charges you $24.37. What did he do wrong? Explain.

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Evaluating Expressions Welcome to Algebra! You are here! Now, you will start to see letters in the problems called Variables. Variables

represent a numerical value. Sometimes, you are given the value of these variables and other times (later in this

course), you will have to solve it to find the value of the variable.

For now, whenever you see the word “Evaluate”, think plug in the “Value” and Simplify problem. It’s Easy!!!

Plug it in & Solve!

1. x2 – 2x + 3 when x = 4 2. –b2 – 4ac when a = 2 b = 3 c = -1

3. (m2 – 4)2 when m = -3 4. 3r – 2(r2 + 5) when r = 5

9r

5. 2

7

y

y when y = -8 6. 2(8 – B)2 ÷ B – 2 when B = 4

7. A(4 – 2)2 ÷ A – 4 when A = 6 8. 64 – 18 ÷ 9 • 4 ÷ 2 + 20 =

9. 4x2 – 2x + 3 when x = 2 10. –3b2 – 4ac when a = 2 b = 3 c = -1

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11. (m2 – 4)2 when m = -4 12. 3r – 2(r2 + 5) when r = 3

4r + 7

13. 8

132y

y when y = -3

14. 2 x 32 ÷ 7 =

15. 6(4 – 2)2 ÷ 6 – 2 =

16. (9 – 7)2 – 3 =

5

17. 64 – 18 ÷ 9 x 4 ÷ 2 + 21 =

18. 7(32 ÷ z + z) when z = 4

19. Which is correct? Explain why.

(9 – 7)2 – 5 ÷ 5 = 3 or (9 – 7)2 – 5 ÷ 5 = 5

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20. Using +, - , x, and ÷ in the correct order, make an equation using 7, 26, 46, and 15 to

equal 160.

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All Things Shall be Distributed Equally!

If you really understand the Order of Operations, then you’ll notice something weird. Consider

the following problem:

3 (4 + 2)

Now if we follow the Order correctly, we first add up 4 and 2. So now we have:

3(6)

And 3 times 6 equals 18. So the answer is 18.

But we could also do this:

3(4 + 2) = 3(4) + 3(2)

If we did that and multiplied the 3 times the 4 then multiplied the 3 times the 2, we could add

them together and get: 12 + 6 = 18! We get the same answer! That’s because of a thing

called the Distributive Property. It’s very important in Algebra. We use it all the time.

You may ask, “Well why do I need to do that? I can just follow the order of operations”

But sometimes in Algebra we don’t have all the numbers. For example, if the problem above

looked like this:

3(x + 2)

I can’t add x + 2 because I don’t know what x is. So in a case like this we need to Distribute.

3(x) + 3(2)

And you wind up with: 3x + 6 and that’s as far as I can go until you tell me what x is.

The Distributive property works great if you have a whole bunch of letters also. (those letters

are called variables by the way….remember?)

-4(x + 2y + 3z) ( -4)(x) + -4(-2y) + (-4)(3z)

-4x + 8y -12z

---------------------------------------------------------------------------------------------- Now you try: 1. 2(b + 5) 2. 4(x + 3) 3. -7(1 + g) 4. -4(1 + y) 5. -6(5x - 2) 6. -9(6m - 7) 7. -7(-x - 4)

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8. -4(y – 12) = 9. –(2x – 7) = 10. -10(2x +4y – 8)=

11. 1

2(4x 24)= 12. )168(

4

1x = 13. )123(

3

2x

14. 2(x2-8) – 3(20x) = 15. 20(x21

2x 3) 16. 5(-20z – 10 + 5) =

17. –(x-10)= 18. -3(14 + 3x)=

19. 2

3(9y2

1

3y3

5)= 20. (2 + 3x)(5 – 6y)= Hint: it is a 2 in 1 dist. Problem

Distributive Property in Reverse-

21. (14x – 49)= ? ( ? - ?) 22. (5y3 20y2 60) = ?( ? - ? + ?)

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What are the terms? An Introduction to Combining Like Terms

If we want to know how to combine like terms, it’s probably important to know what a term is. A term can be a

number, or it can be a variable. It could also be the product of several numbers or variables. The way to tell the

difference between two terms is that they’re separated from each other by a + or sign in an expression.

For example, in the expression: 3 + 4x + 5yzw

3, 4x, and 5yzw are all terms.

But they are not like terms.

Like terms have the same variables with the same exponents.

6, 7, 9, -21, -4, 0, 1 are all LIKE terms

-3x , x, 21x, 4x, -x are all LIKE terms because they all have the same variable, x, with the same power

-4x2, 12x2, -x2, x2 are all LIKE terms because they all have the same variable, x2, with the same power

x2y, 3x2y, -2x2y, 42x2y are all LIKE terms because they all have the same variable combo of x2y

In like terms, the variable portions must contain the same letters with the same exponents.

Thus 4xyz2 and –3xyz2 are like terms, but 4xy2z and –3xyz2 are not like terms.

ONLY LIKE TERMS MAY BE ADDED OR SUBTRACTED WITH EACH OTHER.

Like terms differ only in their numerical coefficient. The coefficient is just the number that’s next to the variable. The

numerical coefficient is customarily written first. Thus 2x is preferred to x2.

Addition and subtraction of like terms can be accomplished by combining their coefficients. To simplify an expression

means to combine all like terms in the expression. Nothing happens to the variable. Only the coefficient is effected.

Example Simplify by combining like terms, if possible.

-3a + 4b –2 - a + 4b – 7

-3a and –a are like terms, so we start by combining those two: -3a – a = -4a

4b and 4b are like terms so let’s put those together: 4b + 4b = 8b

-2 and -7 are like terms so let’s put those together: -2 – 7 = -9

That’s all we can combine, so that becomes our answer: -4a + 8b – 9

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Let’s try some together:

Simplify by combining like terms

a) 6x - 8y – 20x + 4y b) 5a - 10a2 - 10a + 3a

2

Using the distributive property to simplify like terms

a(b + c +d + …) = ab + ac + ad + …

The distributive property allows us to remove grouping symbols by multiplying a to each term of the expression

within the grouping symbol, b + c + d + …

Example Simplify the expression: -2(1 – a) - 3(2a – 1)

Note that there are two terms, -2(1 – a) and –3(2a – 1)

Apply the distributive property first: -2(1 – a) = -2 + 2a and –3(2a – 1) = - 6a + 3

Now combine what’s left: -2 + 2a – 6a + 3

-2 and 3 are like terms: -2 + 3 = 1 2a and -6a are like terms: 2a – 6a = -4a

That’s as far as I can go. So my final answer is: -4a + 1

------------------------------------------------------------------------------------------------------------------------------

Now you try! Simplify the following phrases

1. -4y2 – (-5y2) + 9y2 2. 6ab – 8ab – 3ab 3. -3p – p – (-9p) + (-11p) + 7p

4. 4r – 8p – 6r + 5p 5. -5a – 6ab + 10ab + 2a 6. 6g – f + 7f – 18g + 3f

7. x4y2 + (-9x2y4) – (-3x2y4) – 4x4y2 8. 17a2b3 + 11a2 – 14a2b3 – 4b3 – 3a2b3 9. 3(x – 7) + 4x

10. –(x – 7) – 12 11. -2(c – 5) – 3c + c2 12. –(x + 4) – (4x + 2)

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13. 3(-x2 + x) – 12x2 + 9 + 2x 14. x4y3 + 3x3y4 – 2x4y3 – (x + 3)

15. –(-5 – x) 16. 2(c + 7) – (c2 – c)

17. –(-x + 3) 18. 9(c + 3) – 9(c – 6)

19. 3(4 – x) + x2 20. -2(x2 – 5) – 4x2

21. -6(1 – 2a) - 5(1 - a) 22. –5x – 2(3 – x) – 4(x + 7) - 6

23. -3y – 4(-5y – 1) – 4(1 – y) + 2(2y – 5) 24. 5a – 2(b – 3a) + 2(7a – b)

25. Evaluate the expressions for the given value of x.

a. -x(8 – x) + 2x when x = 2 b. 6(-x – 3) – x(9 + x) when x = 4

Now simplify the expression first, and then evaluate the expression for the given value of x of the two problems above.

Which way is easier? Explain.

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Let’s try combining again Simplify the following phrases

1. 18f – 13f – 19f 2. 9e + 19e4 - 10e3 - 6e + 16e2 + e

3. 4u2 - 3 + 7 + 5u 4. 8w - 13w2 - 2 - 17w2 + 7 + 14w + 10

5. 9g2 + 19g2 - 18g – 3 6. 16j2 + 11j3 + 12j2 + 19j

7. 8c2 + 11c - 2c + 4 + 16 - 10c2 - 13c2 8. 18t - 7t + 6 - 17t - 14t

9. 10d - 1 + 13d + 9d2 + 18 + 3d 10. -5b2c3 – 7bc – 8b3c2 + 7b2c3 – 4b3c2

11. -2(x – 6) – 3x 12. –(5x + 4) – (3x + 3)

13. 2(-x2 +2x) – 15x2 + 9 – 7x 14. – (x + 3)

15. –(-7 – x) 16. 2(b + 10) – (b2 – 3b)

17. –x + 3xy – xy + 7x + 4xy 18. 6(v + 4) – 4(v2 – 6)

19. -7(-6x + 7) – (9 – 3x) 20. -3(-10x – 7) – 10(x + 1)

21. Ashlen and Ines collect stamps. Ashlen has x amount of stamps. If Ines has 5 times as many stamps as Ashlen, then

how many stamps do they have together?

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Combining Advancement Review (get that Black Belt!)

Do work on SEPARATE SHEET OF PAPER

1. 4u - 6u3 - 11u2 + 10u

2. 7 + 12 + 5f

3. 1 - 13e + 9e2 + 18e2 - 3e + 19

4. 8m2 - 15 - 16m + 17m + 14m2

5. 17s + 13s

6. 2 + t2 + 16t + 15 - 10 - 12t

7. 17r2 + 4 + 18r2 - 7r2 - 9r + 14 - 13r

8. 8k2 + 19k + 5k4 - 2k - 6k4

9. 11 - 3 - 18v - v + 15v

10. 12 - 19z + 11 - 6z

11. 16h4 + 17h2 + 3h - 2h - 14h2 - 13h4 - 4h

12. 7g + 10g + 9g

13. 8 - 5 + 17d2 + 5d2 - 6d + 7d

14. 19n - 10 + 18n - 13n - 1

15. 14 + 4q - 8 + 12q2 + 15q + 2q2 + 11

16. 9j - 16j2 + 3 + 6j + 12j2 - 1

17. 3 + 8w + 16w2 - 9w

18. 10x - 14 + 13x

19. 18b4 + 15b2 - 7b + 19b - 5b2 + 4b2

21. -4(x + 3) + 2x + 5

23. -5(-x – 8) – 3x – 4x – 5x – 7

20. 2p - 17p

22. –(x – 7) + 3(2x + 5)

24. 7(b – 3) – (b + 7)

Evaluate the following expressions:

1. 6b2 – 5b + 2b when b = -2 4. 12 – 6 ÷ 2 • 8 ÷ 2 + 2 =

2. -3 – 3 + 6 – 5 + 3(-3) = 5. a

acb

2

42

when a = -1 b = -6 c = 5

3. 2(4 – 6) • (6 ÷ 2) = 6. -7(x – 1) – 2 + 2x ÷ x when x = 5

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ANSWERS- BLACK BELT Packet

Fundamentals- Combining

ADDING POSITIVE AND NEGATIVE NUMBERS

1) −6 2) −4 3) −3 4) 14 5) 2 6) 5 7) 19 8) 7 9) 10 10) 1

11) 54

54 12) 24

13) -15

A

14)

-18

-18 15) 35 16) 90

17) -6

18) -6 -6

-6

19)

-30 20)

27

21) -18 22) 50 23) -12 24) 32

The Positive & Negative Number Connection

1. -10 2. 6 3. -7 4. -17 5. -`12 6. -12 7. -19 8. -85 9. -69 10. -13 11. -150 12. -5

13. -128 14. 95 15. -15 16. -7 17. -216 18. 240 19. -336 20. 11 21. 9 22. 19 23. -1200 24.

-4.67 25. -5 26. -72 27. -28 28. -13,200 29. Negative 30. Positive 31. # of negative

numbers 32. -11/7 33. 115/32 34. 30/49 35. 14/25 36. -44/15 37. 2/21 38. 2/111

39. -23/9 40. 125/24

What’s the Order?

1. 11 2. 8 3. 16 4. 18/7 5. 42 6. 27 7. 10 8. 3/2 9. 250/9 10. 6 11. 0 12. 18 13. 88 14. -

1/2 15. 9 16. 25/3 17. 64 18. Bottom one first

Evaluating Expressions

1. 11 2. -1 3. 25 4. -1 5. 1/64 6. 6 7. 0 8. 80 9. 15 10. -19

11. 144 12. -1 13. 4 14. 18/7 15. 2 16. 1/5 17. 81 18. 84

19. (9 – 7)2 – 5 ÷ 5 = 3 because it follows the order of operations and divides 5 by 5 before

subtracting

20. (46 – 26) (15 – 7) = 160

All Things Shall Be Distributed Equally 1. 2b + 10 2. 4x + 12 3. -7 – 7g 4. -4 – 4y 5. -30x + 12 6. -54m + 63 7. 7x + 28 8. -4y + 48 9. -2x + 14 10. -20x – 40y + 80 11. 2x – 12 12. 2x – 4 13.

2x – 8

14. 2x2 – 16 – 60x 15. 20x2 – 10x + 60 16. -100z – 50 + 25 17. –x + 10 18. -42 – 9x

19. 15

6

9

26 2 yy 20. 10 – 12y + 15x – 18xy 21. 7(2x – 7) 22. 5(y3 – 4y2 + 12)

20

What are the Terms?

1. 10y2 2. -5ab 3. P 4. -2r – 3p 5. -3a + 4ab 6. -12g +9f 7. -3x4y2 – 6x2y4

8. 11a2 - 4b3 9. 7x -21 10. –x – 5 11. C2 – 5c + 10 12. -5x – 6 13. -15x2 +5x + 0

14. –x4y3 + 3x3y4 - x – 3 15. 5 + x 16. –c2 + 3c +14 17. X – 3 18. 81 19. x2 = 3x + 12

20. -6x2 + 10

21. 17a – 11 22. -7x – 40 23. 25y – 10 24. 25a – 4b 25. A. -8 b. -94 simplified

first X2 – 6x ; -x2 =15x -18

Let’s Try Combining Again

1. -14f 2. 19e4 – 10e3 + 16e2 + 4e 3. 4u2 + 5u + 4 4. -30w2 + 22w + 15

5. 28g2 – 18g – 3 6. 11j3 + 28j2 + 19j 7. -15c2 + 9c + 20 8. -20t + 6

9. 9d2 + 26d + 17 10. -12b3c2 + 2b2c3 – 7bc 11. -5x + 12 12. -8x – 7

13. -17x2 – 3x + 9 14. -x – 3 15. x + 7 16. -b2 + 5b + 20 17. 6xy + 6x

18. -4v2 + 6v + 48 19. 45x – 58 20. 20x + 11 21. 6x

Combining Advancement Review

1. -6u3 - 11u2 + 14u 2. 5f + 19 3. 27e2 - 16e + 20 4. 22m2 + m – 15 5. 30s

6. t2 + 4t + 7 7. 28r2 - 22r + 18 8. -k4 + 8k2 + 17k 9. -4v + 8 10. -25z + 23

11. 3h4 + 3h2 - 3h 12. 26g 13. 22d2 + d + 3 14. 24n – 11 15. 14q2 + 19q + 17

16. -4j2 + 15j + 2 17. 16w2 - w + 3 18. 23x – 14 19. 18b4 + 14b2 + 12b

20. -15p 21. -2x – 7 22. 5x + 22 23. -7x + 33 24. 6b – 28

1. 30 2. -14 3. -12 4. 2 5. -2 6. -28