In algebraic expressions, like terms are terms
that contain the same variables raised to the
same power. Only the coefficients of like terms
are different.
Since adding or subtracting unlike terms is like
mixing apples and oranges -- only like terms
can be combined. To combine like terms, add
the coefficients and multiply the sum by the
common variables.
Like terms are terms that contain the same
variables raised to the same power. Only the
numerical coefficients are different. In an
expression, only like terms can be combined.
We combine like terms to shorten and simplify
algebraic expressions, so we can work with
them more easily. To combine like terms, we
add the coefficients and keep the variables the
same. We can't combine unlike terms because
that's like trying to add apples and oranges!
Look at these 10 terms. Let's find all the like
terms that can be combined.
all these terms have x2y
all these terms have xy2
this is the only x2yz term
this is the only xy term
all these terms have x2y2
this is the only xy2z term
Be careful when combining!
Terms like x2yz and xy2z look a lot alike, but they aren't
and cannot be combined. Write the terms carefully when
working out problems.
Don't overlook terms that are alike!
Terms obey the associative property of multiplication that is, xy and yx are like terms, as are xy2 and y2x.
The expressions on the right have had
their like terms combined. Match each
expression on the left with an expression
on the right. Type the letter of the
correct expression in the box.
a.
b.
c.
d.
e.
f.
g.
Whenever a problem can be simplified, you
should simplify it before substituting numbers
for the letters. This will make your job a lot
easier! To simplify an algebraic expression:
Clear the parentheses. Before you evaluate an
algebraic expression, you need to simplify it.
This will make all your calculations much
easier. Here are the basic steps to follow to
simplify an algebraic expression:
1. remove parentheses by multiplying factors
2. use exponent rules to remove parentheses
in terms with exponents
3. combine like terms by adding coefficients
4. combine the constants
Let's work through an example.
When simplifying an expression, the first thing
to look for is whether you can clear any
parentheses. Often, you can use the
distributive property to clear parentheses, by
multiplying the factors times the terms inside
the parentheses. In this expression, we can
use the distributive property to get rid of the
first two sets of parentheses.
Now we can get rid of the parentheses in the
term with the exponents by using the
exponent rules we learned earlier. When a
term with an exponent is raised to a power,
we multiply the exponents, so (x2)2 becomes
x4 .
The next step in simplifying is to look for like
terms and combine them. The terms 5x and
15x are like terms, because they have the
same variable raised to the same power -namely, the first power, since the exponent is
understood to be 1. We can combine these
two terms to get 20x.
Finally, we look for any constants that we can
combine. Here, we have the constants 10 and
12. We can combine them to get 22.
Now our expression is simplified. Just one
more thing -- usually we write an algebraic
expression in a certain order. We start with
the terms that have the largest exponents and
work our way down to the constants. Using
the commutative property of addition, we can
rearrange the terms and put this expression in
correct order, like this.
1. parentheses.
2. Combine like terms by adding coefficients.
3. Combine the constants.