Today we are going to talk about the distributive property. Here’s our example: Two times five X minus two Y times three. That’s ten X minus four Y plus 6. Now let’s go over the rules for the distributive property. The rules for the distributive property are very simple. We are going to multiply each term by the led number or led coefficient in front of our parenthesis. So we are multiplying. That’s one of the biggest mistakes I see students commit. They add instead of multiplying. Now let’s go back and break it into slow mo. We are going to take the two and multiply it by each term. Two times five X which equals 10 and I bring down my X and two times negative two Y so I have a negative and the two times two Y is four Y and I bring down the variable. Then I take the two times the positive three I take two bring down my positive, two times three gives me positive six. So there is the distributive property. Now let’s look at one that has a variable in it. We are going to distribute the three X into a trinomial, because we have three terms. So we are going to take three X times two X squared. So we take the two times the three, which gives us six times an X squared which gives us an X cubed because we are going to add the exponents. Now we take the three X minus three Y three times three is X just gives us an XY Now the final term I’m going to bring down my addition Three X times positive eight is twenty four there are no other variables so I will tack on my X That is the distributive property
Distributive Property Definition
Disributive Property Definition
Multiply the led coefficient (2), by the numbers inside the parentheses one at a time.
The numbers inside the parentheses cannot be added together because they are not like terms
Add similar exponents
Same rule applies with exponents, multiple the led coefficient, which in this example is 3x, by the numbers inside the parentheses one at a time.
Add similar exponents.
What is the distributive propery?
A formal definition of the Distributive Property would sound something like this," The distributive property states that multiplying a sum by a number gives the same result as multiplying each number, and then adding the products together."
In other words you can add the numbers in the parenthesis, and then multiply, or multiply the number outside the parenthesis, and then add.
In either case you get the same result. This example is called the Distributive property over addition.
For example 4(2+3)
4(2+3)= 4 * 5 = 20 (add then multiply)
or 4(2+3)= 4*2 + 4*3 = 8 + 12 = 20 (multiply then add)
If you add then multiply, or multiply then add you get the same answer.
The Distributive property over subtraction works the same way.
You can subtract the numbers inside the parenthesis and then add, or multiply the number outside the parenthesis and then subtract.
For example: 4(5-2) = 4(3) = 12 (Subtract then multiply
or 4*5 - 4*2 = 20-8 =12 (Multiply then subtract)
The Distributive property is written as:
a(b + c) = ab + ac
When using the Distributive Property follow these rules.
1. Multiply each term inside the parenthesis by the lead term, which is the number outside the parentheses
2. Do not combine unlike terms inside the parenthesis, and the multiply this term by the lead term.
3. Do not multiply the lead term, and then add the lead term to the next term or terms.
For example,it would be incorrect to remove the parenthesis and then add.
For example: 4(5 +4x)= 4*5 + 4+4x
20+8x=28x this is incorrect.
According to the distributive property you must multiply the lead terms by the terms inside the parenthesis.