WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com; this lesson is on distributive property.
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When you are using distributive property, you are multiplying everything inside the parentheses to the number on the outside.
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You are going to distribute the outside number to everything inside the parentheses.
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Here are just some examples with variables.
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A and B, C and D, are all variables.
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If I have the outside number is A, I am going to multiply it to the inside number of B.
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This is just going to become A times B which is AB.
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Here I have two numbers inside the parentheses.
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You are going to take this outside number; multiply it to both numbers.
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First I am going to multiply it to B.
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It is going to be... A times B is AB.
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Then I have the plus to separate them.
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Then A, the outside number, to that number.
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It is going to be A times C which is AC.
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This one, there is three numbers on the inside.
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I take my outside number, multiply it to that one.
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It is going to be A times B; separate using that plus; A times that one; it is AC.
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Then I have a third one; I separate it with that plus; A times D.
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You are just multiplying the outside number to everything inside the parentheses.
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Some examples; 4 times 2 plus 3.
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Here you can go ahead and solve inside the parentheses first before multiplying the 4.
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You can solve this out by doing 4 times... 2 plus 3 is 5.
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Then this 4 times 5 is 20.
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If you want to use distributive property because sometimes you do have to use distributive property,
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you are going to take the outside number of 4.
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Multiply it to the first number 2; it is... 4 times 2 is 8.
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I have a second number; I am going to separate that by that plus sign.
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4 times that number is 12; 8 plus 12 is 20.
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You are going to get the same answer.
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We notice that this one is a lot easier.
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If you can solve inside the parentheses first, then go ahead and do it that way.
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But sometimes you have to do it this way.
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You have to use distributive property just like in the next example.
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2 times A plus 6; here inside the parentheses, A plus 6.
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I can't solve that out because this one A is a variable and this is a number.
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I can't combine those; this is not 6A.
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This A plus 6 is just A plus 6.
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In this case, since I can't solve within the parentheses, I have to use distributive property.
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You are going to take the outside number of 2.
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Multiply it to the first number or letter of A.
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That becomes 2A; 2 times A is 2A.
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You still have a second number.
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You are going to separate it; you are going to write your plus sign.
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Then take your outside number; multiply it to that second number.
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2 times 6 is 12; right here, 2A plus 12.
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Again I can't solve that out because I have a variable here and this one does not have that same variable.
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My answer will just be 2A plus 12.
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You are going to leave it like this, 2A plus 12.
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Few more examples; this one right here.
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Again I can't solve within the parentheses; I have to use distributive property.
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Take the outside which is C; multiply the first number inside.
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C times 5 is 5C; 5C.
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When you have a number multiplied to a variable, you are just going to write it together like this.
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5C, with the number first; instead of C5, you are going to write 5C.
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I have a minus to separate those two; then this one times the second one.
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CA or you can do AC; it doesn't matter.
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When you have a variable times a variable, you are just going to write them together.
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It is CA or AC; we can't subtract these together because they have different variables.
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So that is just my answer.
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The next one, 10 times 8 minus 3; here I can solve within the parentheses.
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I can do 10 times... 8 minus 3 is 5; 10 times 5 is 50.
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Or if you have to use distributive property, take the outside number.
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Multiply it to that first one; this is 80; write this sign to separate them.
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Then I am going to do 10 times the second number which is 30.
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Then 80 minus 30 is 50.
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You have to make sure that these numbers are the same; that is your answer.
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This example right here, 4 times B plus C.
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Again you take the 4, the outside number.
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You are going to multiply it to that first number inside or in this case letter.
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4 times B is 4B; again number times a letter.
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You are just going to write it together with the number in the front.
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It is 4B plus... multiply it to that one, the second one.
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4 times C is 4C; I can't combine them; they have different variables.
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That is my answer.
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Next example, 9 times 5 minus D; I can't solve within the parentheses.
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Take the outside number; multiply it to that first one of 5.
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9 times 5 is 45; you are going to write this sign to separate them.
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Then 9 times D which is 9D; sorry... 9D.
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I can't combine them; that is my answer.
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Let's do a couple more.
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7 times M minus 8; let me just write that again.
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Here again I can't solve within the parentheses because I have a variable, M, minus 8, a number.
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This one doesn't have the same variable.
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In this case, I have to use distributive property.
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I am going to take my outside number which is 7.
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Multiply it to everything inside the parentheses.
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I take the 7; multiply it to M, the first thing in there.
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7 times M is 7M.
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Again you have a number times a letter or a variable.
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When you do that, you are going to write it 7M with the number first.
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Then you are going to write this sign to separate them.
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You are going to take the outside number and multiply it to that second number in there.
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7 times 8 is 56; I look at this; I can't combine them.
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I can't subtract them because this has a variable of M and this one doesn't.
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That becomes my answer; I am just going to leave it like that.
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My next example, X plus Y plus 3.
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For this one, I have three different things I have to distribute the outside number to.
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I am going to take the 2; multiply it to the X first.
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2 times X is 2X; separate it with that sign, plus.
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2 times the Y is 2Y; again I have to separate it with that sign.
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Then 2 times the 3 which is 6; can I combine any of these?
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No, none of these are like terms because this has a variable of X.
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This one has a Y; this one doesn't have a variable.
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You are just going to leave it like that as your answer.
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Again when you are using distributive property, you are going to take the outside number,
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multiply it to each thing inside the parentheses, separate them with a sign--with the plus or the minus sign.
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After you distribute that, see if you can combine like terms together.
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If not, then that is your answer.
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That is it for this lesson; thank you for watching Educator.com.