Combine Like Terms and
Distributive Property
Mr. Stallings
December 2011
Combine Like Terms and
Distributive Property
In this lesson, you will be shown how to
combine like terms along with using the
distributive property.
Terms in an algebraic expression are
separated by addition or subtraction signs.
How many terms are in this expression?
So, what are like terms?
Like terms are terms that look alike.
More specifically, Like Terms are terms that
have the same variable raised to the same
power (exponent).
Now, let’s give this a try.
Combine like terms.
A. 14a – 5a
9a
Identify like terms.
B. 7y + 8 – 3y – 1 + y
Identify like terms ; the
coefficient of y is 1, because
1y = y.
5y + 7
Combine coefficients: 14 – 5 = 9
Combine coefficients: 7 – 3 + 1 = 5
and 8 – 1 = 7
Combine like terms.
C. 4q – q
3q
D. 5c + 8 – 4c – 2 – c
6
Identify like terms; the
coefficient of q is 1, because
1q = q.
Combine coefficients: 4 – 1 = 3
Identify like terms; the
coefficient of c is 1, because
1c = c.
Combine coefficients: 5 – 4 – 1 = 0
and 8 – 2 = 6
Combine like terms.
E. 4m + 9n – 2
4m + 9n – 2
F. 5m – 7m – 8 + 4
-2m – 4
No like terms.
Remember, to simplify an expression
means to perform all possible
operations, including combining like
terms.
In other words, simplify means solve!
The Distributive Property is an algebra property which is
used to multiply a single term and two or more terms
inside a set of parentheses.
For any numbers a, b, and c,
a(b + c) = a(b) + a(c)
and
a(b – c) = a(b) – a(c)
Distribute
A. 6(x - 3)
6x - 18
B. -2(y + 1)
-2y + (-2)
C. -3(a - 1)
-3a – (-3)
Now we will use the distributive
property first, then combine like terms
second.
1. Simplify 6(5 + n) – 2n.
6(5 + n) – 2n
6(5) + 6(n) – 2n
Distributive Property.
30 + 6n – 2n
Multiply.
30 + 4n
Combine coefficients 6 – 2 = 4.
2. Simplify 3(c + 7) – c.
3(c + 7) – c
3(c) + 3(7) – c
Distributive Property.
3c + 21 – c
Multiply.
2c + 21
Combine coefficients 3 – 1 = 2.
Simplify.
3. 4(3x + 6)  7x
4. 6(x + 5) + 3x
4. 5(2x - 3) + 4x
10x – 15 + 4x
14x - 15