Download Module 2 Pre-Algebra Activities Weeks

Module 3 1st nine weeks Pre-Algebra Order Of Operations/
Multi-Step Linear Equations
Activity 2.3 Weeks 6-8
Simplifying Algebraic Expressions
Learning Objectives
After completing this tutorial, you should be able to:
1. Identify a term, coefficient, constant term, and like terms.
2. Combine like terms.
3. Simplify an expression using distributive property and combining like
terms.
Term
A term is a number, variable or the product of a number and variable(s).
Examples of terms are
,
,
,z
Coefficient
A coefficient is the numeric factor of your term.
Here are the coefficients of the terms listed above:
Term
Coefficient
3
5
2
z
1
Constant Term
A constant term is a term that contains only a number. In other words, there
is no variable in a constant term.
Examples of constant terms are 4, 100, and -5.
Like Terms
Like terms are terms that have the exact same variables raised to the exact
same exponents.
One example of like terms is
. Another example is
.
Combining Like Terms
You can only combine terms that are like terms. You think of it as the
reverse of the distributive property.
It is like counting apples and oranges. You just count up how many variables
you have the same and write the number in front of the common variable
part.
Example 1: Simplify
by combining like terms.
Are there any like terms that we can combine?
It looks like it. Both terms have the same variable part, a.
*Use distributive prop. to combine like terms
Example 2: Simplify
by combining like terms.
Are there any like terms that we can combine?
It looks like it. Two terms have the same variable part, b. The other
pair of terms are constant terms that can be combined together.
*Use distributive prop. to combine like terms
From here on out I will not be showing the distributive property step when
combining like terms. I will go right into adding or subtracting the
coefficients of the like terms. I showed you the distributive property in the
above examples to give you the thought behind combining like terms.
Example 3: Simplify the expression
.
It looks like we have two terms that have an x squared that we can
combine and we have two terms that have an x that we can combine.
The poor 5 does not have anything it can combine with so it will have
to stay 5.
Grouping like terms together and combining them we get:
*Combine the x squared terms together
and then the x terms together
Example 4: Simplify the expression
.
*A - outside a ( ) is the same as times (-1)
*Distribute the (-1) to EVERY term inside ( )
*Multiply
Basically, when you have a negative sign in front of a ( ), like this
example, you can think of it as taking a -1 times the ( ). What you end
up doing in the end is taking the opposite of every term in the ( ).
Example 5: Simplify the expression
.
Let's first apply the distributive property (found in Tutorial 8:
Properties of Real Numbers) and see what we get:
*Dist. 2 to EVERY term of 1st ( )
*Dist. -3 to EVERY term of 2nd ( )
*Multiply
Regrouping and combining like terms we get:
*x is distributed to the 1st 2 terms
*Reverse Dist. Prop with x
*Subtract
Example 6: Write the following as an algebraic expression and
simplify if possible.
Add 3a + 9 to 7a - 2.
Basically we will be adding these two expressions together.
Writing this as an algebraic expression we get:
Regrouping and combining like terms we get:
Example 7: Write the following as an algebraic expression and
simplify if possible.
The sum of 5 times a number and 2, subtracted from 12 times a number.
x is representing the unknown number. The sum of 5 times a number
and 2 can be written as 5x + 2. From there we need to subtract that
from 12x.
Writing this as an algebraic expression we get:
Using the distributive property (found in Tutorial 8: Properties of
Real Numbers) and then combining like terms we get:
Practice Exercises for activity 2.3
Name the coefficients.
1.) 3x + 5y -3
3.) 6xy – 5xy
2.) 2x -7
Simplify each expression.
4.) 12a + a
8.) 8n + 8y + 3n
5.)5a + 8a
6.) 4a -3 + 5a
9.) 18 + 6(9k – 13)
7.) 2g + 3(g + 5)
10.) 2x – 6 + 3x - x