Distributing
Objective
Know how to use the distributive property
Example
(f-1)(p-2)
Answer: fp - 2f - p + 2
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Explanation
In math, we always want to make our answers as simple as possible. Sometimes that means leaving an answer with parenthesis, sometimes that means getting rid of the parenthesis. The distributive property shows you how to get rid of parenthesis.
1.) When you simply have a coefficient in front of a group of parenthesis, you multiply with everything in the parenthesis.
-3(m-s)
= -3 x m + -3 x -s
= -3m + 3s (-3 x -s becomes +3s because a negative times a negative gives a positive)
Answer: -3m+3s
2.) When you have a group of parenthesis times another group of parenthesis, it gets harder. In these cases, every term in the first group of parenthesis must be multiplied by every term in the second group of parenthesis.
If both parenthesis have 2 terms in them, we can use FOIL to help us
First (the first term from both groups of parenthesis)
Outside (the first term from the first group, the last term from the last group)
Inside (the last term from the first group, the first term from the last group)
Last (the last term from both groups of parenthesis)
Lets try FOIL out
(-10-i)(1-m)
First: (-10-i)(1-m)
-10 x 1 = -10
Outside: (-10-i)(1-m)
-10 x -m = 10m
Inside: (-10-i)(1-m)
-i x 1-= -i
Last: (-10-i)(1-m)
-i x -m = im
put it all together
-10 + 10m - i + im
lastly, put it in alphabetical order, putting terms with more variables first
im - i + 10m -10
Answer: im-i+10m-10
For a Khan Academy video, click here
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Examples
Example 1
n(r+y)
= n x r + n x y
= nr + ny
Answer: nr+ny
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Example 2
(f-4)(p-4)
F: fp
O: -4f
I: -4p
L: 16
Answer: fp-4f-4p+16
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Practice your skills
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Ready?