Basic Math Distributive Property

Welcome back to Educator.com; this lesson is on distributive property.0000

When you are using distributive property, you are multiplying everything inside the parentheses to the number on the outside.0010

You are going to distribute the outside number to everything inside the parentheses.0022

Here are just some examples with variables.0028

A and B, C and D, are all variables.0032

If I have the outside number is A, I am going to multiply it to the inside number of B.0035

This is just going to become A times B which is AB.0042

Here I have two numbers inside the parentheses.0050

You are going to take this outside number; multiply it to both numbers.0055

First I am going to multiply it to B.0060

It is going to be... A times B is AB.0063

Then I have the plus to separate them.0068

Then A, the outside number, to that number.0072

It is going to be A times C which is AC.0075

This one, there is three numbers on the inside.0082

I take my outside number, multiply it to that one.0087

It is going to be A times B; separate using that plus; A times that one; it is AC.0092

Then I have a third one; I separate it with that plus; A times D.0102

You are just multiplying the outside number to everything inside the parentheses.0110

Some examples; 4 times 2 plus 3.0120

Here you can go ahead and solve inside the parentheses first before multiplying the 4.0126

You can solve this out by doing 4 times... 2 plus 3 is 5.0136

Then this 4 times 5 is 20.0142

If you want to use distributive property because sometimes you do have to use distributive property,0148

you are going to take the outside number of 4.0156

Multiply it to the first number 2; it is... 4 times 2 is 8.0159

I have a second number; I am going to separate that by that plus sign.0166

4 times that number is 12; 8 plus 12 is 20.0171

You are going to get the same answer.0181

We notice that this one is a lot easier.0183

If you can solve inside the parentheses first, then go ahead and do it that way.0186

But sometimes you have to do it this way.0192

You have to use distributive property just like in the next example.0195

2 times A plus 6; here inside the parentheses, A plus 6.0200

I can't solve that out because this one A is a variable and this is a number.0209

I can't combine those; this is not 6A.0214

This A plus 6 is just A plus 6.0217

In this case, since I can't solve within the parentheses, I have to use distributive property.0221

You are going to take the outside number of 2.0227

Multiply it to the first number or letter of A.0229

That becomes 2A; 2 times A is 2A.0235

You still have a second number.0242

You are going to separate it; you are going to write your plus sign.0243

Then take your outside number; multiply it to that second number.0248

2 times 6 is 12; right here, 2A plus 12.0253

Again I can't solve that out because I have a variable here and this one does not have that same variable.0261

My answer will just be 2A plus 12.0267

You are going to leave it like this, 2A plus 12.0271

Few more examples; this one right here.0276

Again I can't solve within the parentheses; I have to use distributive property.0283

Take the outside which is C; multiply the first number inside.0288

C times 5 is 5C; 5C.0296

When you have a number multiplied to a variable, you are just going to write it together like this.0302

5C, with the number first; instead of C5, you are going to write 5C.0308

I have a minus to separate those two; then this one times the second one.0316

CA or you can do AC; it doesn't matter.0323

When you have a variable times a variable, you are just going to write them together.0326

It is CA or AC; we can't subtract these together because they have different variables.0329

So that is just my answer.0339

The next one, 10 times 8 minus 3; here I can solve within the parentheses.0342

I can do 10 times... 8 minus 3 is 5; 10 times 5 is 50.0354

Or if you have to use distributive property, take the outside number.0365

Multiply it to that first one; this is 80; write this sign to separate them.0374

Then I am going to do 10 times the second number which is 30.0384

Then 80 minus 30 is 50.0391

You have to make sure that these numbers are the same; that is your answer.0394

This example right here, 4 times B plus C.0402

Again you take the 4, the outside number.0409

You are going to multiply it to that first number inside or in this case letter.0411

4 times B is 4B; again number times a letter.0417

You are just going to write it together with the number in the front.0425

It is 4B plus... multiply it to that one, the second one.0428

4 times C is 4C; I can't combine them; they have different variables.0435

That is my answer.0441

Next example, 9 times 5 minus D; I can't solve within the parentheses.0446

Take the outside number; multiply it to that first one of 5.0457

9 times 5 is 45; you are going to write this sign to separate them.0465

Then 9 times D which is 9D; sorry... 9D.0472

I can't combine them; that is my answer.0492

Let's do a couple more.0497

7 times M minus 8; let me just write that again.0501

Here again I can't solve within the parentheses because I have a variable, M, minus 8, a number.0509

This one doesn't have the same variable.0516

In this case, I have to use distributive property.0520

I am going to take my outside number which is 7.0523

Multiply it to everything inside the parentheses.0527

I take the 7; multiply it to M, the first thing in there.0531

7 times M is 7M.0538

Again you have a number times a letter or a variable.0541

When you do that, you are going to write it 7M with the number first.0546

Then you are going to write this sign to separate them.0551

You are going to take the outside number and multiply it to that second number in there.0554

7 times 8 is 56; I look at this; I can't combine them.0561

I can't subtract them because this has a variable of M and this one doesn't.0571

That becomes my answer; I am just going to leave it like that.0577

My next example, X plus Y plus 3.0581

For this one, I have three different things I have to distribute the outside number to.0590

I am going to take the 2; multiply it to the X first.0598

2 times X is 2X; separate it with that sign, plus.0602

2 times the Y is 2Y; again I have to separate it with that sign.0610

Then 2 times the 3 which is 6; can I combine any of these?0618

No, none of these are like terms because this has a variable of X.0629

This one has a Y; this one doesn't have a variable.0632

You are just going to leave it like that as your answer.0636

Again when you are using distributive property, you are going to take the outside number,0639

multiply it to each thing inside the parentheses, separate them with a sign--with the plus or the minus sign.0643

After you distribute that, see if you can combine like terms together.0654

If not, then that is your answer.0659

That is it for this lesson; thank you for watching Educator.com.0662