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MFM1PI: Foundations of Mathematics
Unit 4: Working with Algebra
Daily Notes
Day
1
2
Date
Topic
Intro to Algebra &
Like Terms
3
Multiplying and Dividing
Monomials
4
Combining Operations
5
Distributive Property Part 1
6
Distributive Property Part 2
7
Algebra Review
8
Unit Test
Day 1: Intro to Algebra
Date:
Algebraic expressions use letters and numbers:
2
4x – 3y + z + 5
Definitions:
An algebraic expression like the one above is called a _______________.
This polynomial has four parts called __________, separated by + or –.
4x2, 3y, and z are called ___________ terms.
The “5” is also a term on its own, and is called a ____________ term.
The letters in a polynomial are called ____________.
The variables in this polynomial are ____ & ____ & ____.
The numbers are called different things depending on what they do:
 The “5” is a ____________ term because it is a non-variable term.
 The “3” and “4” are _____________ because they multiply variables.
 The “2” is an _____________ affecting the variable ____.
 The coefficient of “z” is ____. The exponent of “z” is ____.
Terms with identical _____________ (including __________) are called
_________ terms. They can be combined by adding or subtracting.
Polynomials can be named according to the number of terms they have:
# of Terms
1
2
3
Name
Example
Day 1: Adding Polynomials
Date:
If you want to add polynomials together, you can only put like
terms together. The steps are:
 Mark like terms using underlines, boxes, etc.
 Add the coefficients of the like terms, keep the variable.
Examples:
4x + 3x + 9x
2x + y + 3x + 5y
3x2 + 7x – 4x2 + 9
More Examples:
(4x2 - x + 5) + (9x2 - 2x – 6)
(8x2 + 7x + w) + (w + 2x – 3x2)
Day 2: Subtracting Polynomials
Date:
If you want to subtract polynomials, you can only put like terms
together. The steps are:
 Distribute “–“ signs over any brackets.
 Mark like terms using underlines, boxes, etc.
 Add/subtract the coefficients of the like terms, keep the variable.
Examples:
(6x2 - 2x + 15)
- (9x2 + 2x – 6 )
(2x2 + 8x + y)
- (y + 3x – 3x2)
Examples:
(4x2 - x + 5) - (9x2 - 4x + 1)
(8x2 + 7x + w) - (2w + 2x – 3x2)
Day 3: Multiplying and Dividing Monomials
When multiplying and dividing
monomials, the exponents on the
variables can change. (Whereas
with adding and subtracting, the
exponents never change). You will
have to remember the first two
power rules from the exponents unit.
Steps for multiplying monomials
 Multiply the coefficients
 Add the exponents on the variable
Date:__________________
When multiplying powers,
Add the exponents
(x5)(x3) = x8
When dividing powers,
Subtract the exponents
x5 ÷ x3 = x2
Steps for dividing monomials
 Divide the coefficients, or put the fraction in lowest terms
 Subtract the exponents on the variable
Examples
3x7 × 4x3 =
(-2x)(9x5) =
-2y7 · 3y7 · (-4y7) =
4x10 ÷ 2x-2 =
30𝑥 10
=
12𝑥 7
−12𝑥 7
4𝑥 5
=
Day 4: Combining Operations
Date:__________________
Examples
5)
4𝑎𝑏7
2𝑎5
=
6)
2𝑘ℎ3 𝑗 4
4𝑘ℎ2 𝑗
=
Day 5: Distributive Property Part 1
Date:__________________
Any polynomial can be multiplied by a monomial. Each term in
the brackets will be multiplied by the monomial on the outside.
This kind of multiplying is called distribution.
How it works:
BE[DM][AS] Method
Distributive Method
10(5 – 3)
10(5 – 3)
= 10(2)
= 50 – 30
= 20
= 20
Examples
Day 6: Distributive Property Part 2
Date:__________________
Instead of having just a number on the outside, we can also
have a variable. You’ll have to remember to use your exponent
rules for multiplying with a variable.
Examples
Expand
Expand & Simplify
Day 7: Algebra Review
Date:
Algebra Graphic Organizer
Operation
Steps
Add
 Collect Like Terms
 Combine Coefficients
Subtract
 Distribute “-“ with
brackets
 Collect Like Terms
 Combine Coefficients
Multiply
 Multiply Coefficients
 Multiply Variables
o (Add Exponents)
Divide
 Divide Coefficients
 Divide Variables
o (Subtract Exponents)
Distributive
Property
 Multiply the “outside”
term by each of the
“inside” terms
Simplifying
Expressions
 Do Distributive Property
First
 Collect Like Terms
 Combine Coefficients
Example