Adding Like Terms

1.  Now that we have seen some algebraic
expressions, we need to know how to
simplify them.
 Vocabulary
 Like terms: In an expression, like terms are the
terms that have the same variables, raised to the
same powers (same exponents).
 i.e. 4x and -3x or 2y2 and –y2
 Coefficient: A constant that multiplies a variable.
 i.e. the 3 in 3a or the -1 in –b

2.  In algebra we often get very long expressions,
which we need to make simpler. Simpler
expressions are easier to solve!
 To simplify an expression we collect like
terms. Like terms include letters that are the
same and numbers.

3.  Step One: Write the expression.
4x + 5x -2 - 2x + 7
 Collect all the terms together which are alike. Remember that each term
comes with an operation (+,-) which goes before it.
4x, 5x, and -2x
-2 and 7
 Simplify the variable terms.
4x+5x-2x = 9x-2x = 7x
 Simplify the constant (number) terms.
-2+7 = 5
 You have a simplified expression by writing all of the results from
simplifying.
7x + 5

4.  10x – 4y + 3x2 + 2x – 2y
3x2
10x, 2x
-4y – 2y
 3x2 + 12x – 6y
Remember you cannot
combine terms with
the same variable but
different exponents.

5. Simplify the following:
 5x + 3y - 6x + 4y + 3z
 3b - 3a - 5c + 4b
 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4
 5xy – 2yx + 7y + 3x – 4xy + 2x
A
A
A
A

6.  Simplify the following:
1. 5x + 3y - 6x + 4y + 3z
5x, -6x
3y, 4y
3z
-x + 7y + 3z

7.  Simplify the following:
2. 3b - 3a - 5c + 4b
3b, 4b
-3a
-5c
-3a + 7b – 5c

8.  Simplify the following:
3. 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4
4ab, -ab
-2a2b, 2a2b
5, 4
ab2
3ab + ab2 + 9

9.  Simplify the following:
4. 5xy – 2yx + 7y + 3x – 4xy + 2x
5xy, -2yx, -4xy
7y
3x, 2x
-xy + 7y + 5x

10.  A variable or algebraic expression is an
expression that consists of one or more
________ and _________ along with one or
more numbers ________ _________. variables
(Note: No _______
sign)
arithmetic operations
equal
 To evaluate an expression write the _________,
substitute expression a _______ for each variable, and
_________ the result.
number
simplify

11.  In an expression, like __________ terms
are the terms that
have the same ________, variables
raised to the same
________ power
(same exponents).
 A coefficient is a number that ________ multiplies
a
variable.