This document reviews combining like terms and the distributive property through examples and analogies. It explains that like terms have the same variables and exponents, and can be combined by adding or subtracting the coefficients. Examples are provided such as 2x + 5x = 7x and 3bc - 8bc = -5bc. The document also explains that the distributive property involves distributing a term to each part of a binomial, as shown in the examples 2(3x - 4) = 6x - 8 and (5a + 3b)6 = 30a + 18b. An analogy compares combining like terms to combining people with the same last name.

1. Let’s Review!
We’ve been wrestling with
combining like terms and the
distributive property for a
while now! Let’s show them
what we know!
MS ClipArt

2. Combining Like Terms
• What are like terms?
• Terms are alike if they have the same letter or
letters and exponent.
• Here are examples of like terms:
2x and 5x; 3bc and -8bc;
12x2 and 4x2; 6cd and 9cd
• What makes these terms alike? They have
something in common with each other.

3. • To combine like terms add or subtract the
number in front of the variables or letters.
• For example 2x + 5x. They both have x in
common. So add the 2 and 5. (2 + 5)x = 7x.
• What about 3bc and -8bc? If we add them
together, this is what it looks like:
(3 + -8)bc = -5bc.
• How about 12x2 and 4x2? We do the same
thing. (12 + 4)x2. = 16x2.
• And how about 6cd subtract 9cd?
(6 – 9)cd = -3cd.

4. Think about this:
• Naming this couple
on the left is like
combining like terms.
Their last name is
like the variable or
letter that comes
after the number.
John Smith So 1 Smith plus
Joan Smith MS ClipArt another Smith would
be 2 Smith’s or 1S +
1S = 2S.

5. Distributive Property
• Look at the picture of
the flight attendant.
He is distributing or
giving out soft drinks
on the plane. His job is
to make sure everyone
gets a drink.
• If everyone is given a
soft drink, then the
attendant has used
the distributive
property.

6. Some Examples of the
Distributive Property
Example 2(3x – 4) = 2(3x) + 2(-4) = 6x – 8
Example -4(4 – 3bc) = -4(4) + -4(-3bc) =-16 + 12bc
Example (5a + 3b)6 = (5a)(6) + (3b)(6) = 30a + 18b
In each of these examples we used the distributive
property. After we distributed, there were no like
terms to combine. So we are done. Look at each example
and the final answer and remember the Smith’s