The Distributive Property
The distributive property states that for all real numbers a, b, and c:
Let's look at at example:
Since the 3 is outside the parentheses, we can distribute, or multiply it by every term inside the parentheses, which happens to be the x and the 4. Thus, we get:
In the next example, we must use the Product of Powers Property when we distribute:
Since the 4x is outside the parentheses, we distribute it to the three terms inside the parentheses. Remember, when we multiply with like bases, we add the exponents.
Check out the following video about the distributive property. Watch closely how to combine like terms after distributing!
Distributive property with variables by Khan Academy: https://www.youtube.com/watch?v=wTuMU2B6MF4
FOIL
There is a special method that can be used when distributing two binomials. It is called FOIL and the letters represent:
F - First
O - Outside
I - Inside
L - Last
F - First
O - Outside
I - Inside
L - Last
Let's try an example:
The first thing we need to do is "F" or multiply the first terms together as shown in red:
Using the Product of Powers Property, we get:
Then we need to do "O" or multiply the outside terms together as shown in red:
Notice, we keep the negative sign with the 5 and get:
Next, we need to do "I" or multiply the inside terms together as shown in red:
Keeping the signs, we get:
Finally, we do "L" or multiply the last terms together as shown in red:
Again, keeping the signs, we get:
Putting it all together, we get:
Then, we combine the like terms of -5x and 6x and simplify to:
Watch the following video paying especially close attention to the signs in the second example.
Use FOIL Method to Multiply Polynomials in Algebra by TabletClassMath: https://www.youtube.com/watch?v=bn51ML8jkIs
Practice:
Click on the following link to practice using the distributive property:
https://www.ixl.com/math/algebra-1/distributive-property
Click on the following link to practice using FOIL:
https://www.ixl.com/math/algebra-1/multiply-two-binomials
https://www.ixl.com/math/algebra-1/distributive-property
Click on the following link to practice using FOIL:
https://www.ixl.com/math/algebra-1/multiply-two-binomials
When you have become a master at the distributive property, go back and retake the pre-test. You should score 80% or higher before moving on.
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