Identify Parts of an Expression
Circle all coefficients.
50
17ab
.75x
3𝑚4
111
xy
8z
3
15
2y
1.6bc
25
2
pq
3
36𝑏 2
14
14
8z
3
15
2y
1.6bc
.75x
3𝑚4
111
xy
50
17ab
111
xy
50
17ab
11y
-12xy
Underline all variables.
2
pq
3
25
36𝑏 2
Put a square around all constants. How many terms total are there below?
2y
1.6bc
.75x
3𝑚4
25
2
pq
3
36𝑏 2
14
3
15
8z
Circle all like terms given the following term:

-5xy →
3x
87xy
6𝑥 2 y

8𝒎𝟐 →
14m
-9mn
. 45𝑚2
8𝑚4

11q →
-62q
−7𝑞2
6pq
.123y
2
y
5
.65xy
34n
43q
45xy
18𝑥𝑦 3
3𝑚2
- 𝑚2
21q
11v
10𝑥 2
-q
1 2
𝑚
2
−18𝑞3
Factoring Algebraic Expressions
1. 7xy – 28x + 70
2. 12xyz + 48yz – 120z
3. 10mn – 15
4. 32y-80
5. 12bc – 10c + 8
6. 30𝑑2 – 24d
Expanding Algebraic Expressions
1. 6(-8p + 10)
2. -5(11xy – 7x)
3. 12z(xy + 4y – 10)
4. (-8b + 7)3
5. –x(15y – 2)
6. 7(3pqr – 4pq + 7p)
Simplifying Algebraic Expressions (Combining Like Terms)
1. 8xyz + 6x - 4 – 2x + 8
2. 12 – 8 + 4ab +7
3. 9s - 12𝑠 3 + 6(𝑠 3 – 4s) + 10
4. (7x – 14y) – (– 2x + 8y)
5. 34mn – 14mn + 7 + 2mn
6. 4(10y -3) + 5y
Break-down Real-life Situation
1. Autumn is going to buy gifts for all of her family members for a family reunion. She is going to buy each person 2
keepsakes to remember the event. She knows some of the people who plan on coming won’t actually make it so she
is budgeting for 7 less people. Her budget is $10 per person. Let f represent the number of family members who
plan to attend. Use the expression below.
10 ( 2f – 7 )
a. What does each factor of the expression represent? What does the expression represent?
b. Expand the expression. What does each term of your new expression represent?
2. A homeowner decides to build an extension to their rectangular bedroom. Let y represent the increase, in feet,
of the bedrooms length. The expression 11(y + 5) represents the area of your bedroom, where 11 is the width, if
feet, and (y + 5) represents the extended length, in feet, of the bedroom. Expand the expression. What does each
term in the new expression represent?
Re-writing Expressions
1. Elsa loves to buy new pens! Her favorite brand of pens cost $5.00 per pack. They just came out with new colors
than write in pink and green. Write an expression that represents the total cost, t, of the pens she may buy if p
represents pink and g represents green. Can you write the expression? If so re-write it.
2. Anna says that -10x(4y + 7z – 2) is equivalent to -40x – 70x + 20x. Do you agree? Explain your answer.
3. Kristoff tells Sven that 42abc – 21ac + 28c is equivalent to 7c(6abc – 3ac + 4c). Do you agree? Explain your
answer.
4. Which of the following expressions are equivalent to (6y + 15) – (4 – 8y)?
i.
ii.
iii.
iv.
v.
14y + 11
6y + 15 – 4 – 8y
6y + 15 – 4 + 8y
6y + 15 + (-1)(4 – 8y)
6y + 15 + (-4) – (-8y)
Expressions Unit Test - Things to Know
Do I know how to…..?
 Expand Expressions (distribute)
 Factor Expressions (find the GCF and divide it into expression)
 Re-write expressions in a different form
 Distribute (multiply what is next to the parentheses to everything in the parentheses)
 Use properties of integers correctly (rules for adding and subtracting integers)
 Write algebraic expressions in context to real-life examples
 Explain algebraic expressions in context to real-life examples
 Simplify Algebraic Expressions (combine like terms – add, subtract, match identical variable groups)
 Apply my vocabulary terms (if asked to represent or define a key term, can you?)
…If you don’t, you need to make arrangements to be picked up at 3:45 on Monday so you can stay with Ms. Cahill after
school for a tutoring session (please come prepared with questions and examples you don’t understand)