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Algebra
Maths 8
May 2013
Curriculum Outcomes



B14 add and subtract algebraic terms
concretely, pictorially, and symbolically to
solve simple algebraic problems
B15 explore addition and subtraction of
polynomial expressions, concretely and
pictorially
B16 demonstrate an understanding of
multiplication of a polynomial by a scalar,
concretely, pictorially, and symbolically
Vocabulary…
variable: a symbol that represents an unknown value
For example: x, y, a, b, r, h , etc.
coefficient: A number that precedes a variable in an
expression. The coefficient multiplies by the
variable.
For example if we write 3 times w like 3w. 3 is the
coefficient.
vocabulary…
constant: a quantity that does not change.
example: ½ , -3, 6, 
term: A term consists of a constant, a variable, a
coeffieient which is multiplied by the variable, or two
or more variables are possible.
For example: 3, 4x, 4xy2, and x3 are some terms.
vocabulary…
An algebraic expression: An expression with
one or more terms. There is no solution to an
expression.
Example:
3x – 2
-4x3 – 2y + 3xy -5
vocabulary…
An algebraic equation: Two expressions
separated by an equal sign.
Example:
3x – 2 = 6
-4x3 – 2y + 3xy -5 = 4x – 3y
Think and reflect

4x2 – 3x = 1

3y2 + 5x – 7z + 32c -2
Expression or equation?

3y2 + 5x – 7z + 32c -2
Combine the terms?

3x – 5y3 – 8
Identify the numerical coefficients

3x – 5y3 – 8
Identify the variables

3x –  – 8
Expression or equation?
Identify the constants
A little more vocabulary
Monomial: An algebraic expression which contains
only one term.
Example:
x
Binomial: An algebraic expression the contains only
two terms.
Example:
3x – 2
Polynomial: An algebraic expression with more than
one term.
Example :
5x2 + 2x + 3
Yet more vocabulary
Like terms: Terms where the coefficients are
different, but have the same variable.
Examples:
3x and 2x are like
4x and 5y are not like
x2 and x are not like
ALGETILES
1
x
-x
y
-y
-1
x
y
x
x2
-x2
y
x
xy
-xy
y
y2
-y2
Algetiles are pieces used to
represent algebraic terms
concretely.
Represent these expressions
with Algetiles
x2 + 4x + 3
x
x
1
x
x2
x
1
x
1
x
Practice





Represent the following expressions with
algetiles then draw them onto a paper to
hand in to your teacher.
2x - 3
-x2 - 2
2x2 + 3x + 1
x2 + (-2x) + 1
Practice
2x2 + 3x + 1
x
-1
x
-x2 – 2
x2
x
x2
x2 + (-2x) + 1
x
-1
x
-x2
-1
x2
1
x
-1
x
x
x
x
1
x
-1
-x

2x – 3
-x

Combining Like Terms

If you know a certain distance is 2m and another is
30 cm, then you know the total distance is 2 + 30 =
32 units?


NO – You must express the distances with the same units.
2m + 0.3 m = 2.3 m

Can you add 2 dozen and 5 units to get 7?

NO - 2 dozen plus 5 units = 29

Can you add 5 apples and 3 orages to get 8
appleorages?

NO! You must combine like units and/or objects (like terms)
Combining like terms

If the terms are the same variable and have the same exponent,
you can combine them.
x
x
x
5x
x
x
=
+
x
x
x
x
2x
3x
x

But, if the exponents are different, you cannot combine them.
x
x
x
x
x
x2
x2
+
x
=
x
x2
x
2x
x2
+
2x
Combining like terms

If the terms are positive or negative it will not affect combining
like terms.
x
x
x2
x
x
x2
-x2
« zeros »
If you combine a positive term and a negative
term you get « zero »
x
x2
=
-x2
+
0
1
+
-x
x
x

=
0
+
-1
=
0
Combine like terms to simplify
the expressions
x
x
y
-x
x
-x
x
x
x
x
x
2
x
-1
2
y
1
y2
-1
y
1
-x2
1
y
y2
y
y
y2
-x2
1
Regroupe the terms of the same shape and make « zero» when its
possible.
Combine like terms and
simplify
x
-x2
-x
x2
x
x
y
1
-1
1
-1
y
y2
1
x
x2
x+2
-x2
1
y
y2
-x
2
3y +
y
x
x
y
Identify the « zeros » and
regroup the rest.
x
y
y2