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Welcome to the presentation on multiplying expressions.

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Let's get started.

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So if I were to ask you what x plus 2 times, let me use a

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different color, times x plus 3 equals, at first you'd be like,

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huh, that's a little strange.

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But it turns out that you actually already know

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how to do this problem.

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And it's just the distributive property.

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Because, if I just had -- let me write a different problem

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here -- if I just wrote a let me just make it clear, this is

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a separate problem -- if I just wrote a times x plus 3, you

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know that that's just a x plus, you could say a 3, or

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another way to say that would be 3a, right?

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But as you see, all we did is distribute it, this a times 3.

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All we did is distribute the a times the x and the 3.

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Well, we're going to do the same thing here, but instead

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of a we have x plus 2.

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So let's do that.

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So this would be -- let me switch to green -- we get x

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plus 2, and since I'm using green, I'm just going

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to stay with green.

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x plus 2, let me switch to orange.

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x plus 2 times x plus x plus 2 times 3.

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Does that make sense?

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If that looks a little confusing, just pretend

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like that x plus 2 is the a in this example.

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And all we did is, we distributed it across

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that x plus three.

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And now it becomes a pretty straightforward problem.

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What is -- we do distribution again with each part

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of this problem.

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So, let me stay in orange.

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What is x times x?

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Well that's x squared.

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And then x times 2 -- well, that's 2x.

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So we did this left-hand side already.

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Now we do this right-hand side.

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What's 3 times x?

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Well that's 3x.

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What's 3 times 2?

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Well, that's 6.

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And now we're almost done.

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We could say, oh, we have a 2x here and a 3x here, we can

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simplify and add those together.

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And we know that that equals x squared.

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2x plus 3x is equal to 5x.

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x squared plus 5x plus 6.

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So all we did, there's really nothing new to learn here.

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We just distributed the x plus 2 times each term of x plus 3.

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And we got the second step.

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And then we distributed this x times x plus 2, and this 3

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times x plus 2, and simplify.

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Let's do a couple of problems.

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And hopefully it'll hit the point home.

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Let's say I had 5x plus 9 times 4x minus 2.

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Once again, that equals 5x plus 9.

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I'm just distributing it.

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I want to stay in my color that I'm using, so that's why I'm

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just writing it out like this.

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That equals 5x plus 9 times 4x.

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And then plus, 5x plus 9 times minus 2.

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That minus 2 is here and this 4x is here.

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And now we just multiply it out.

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5x times 4x is 20x squared.

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Hope that makes sense to you; let me write it

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down in this corner.

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5x times 4x is the same thing as 5 times 4 times x times x.

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That equals 20x squared.

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Hopefully that makes sense to you.

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So, going back to the problem.

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5x times 4x is 20x squared plus 9 times 4x is 36x.

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Plus minus 2 times 5x.

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So that's minus 10x.

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And then 9 times negative 2, well, that's minus 18.

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And we're almost done.

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So we get 20x squared.

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And we have 36x.

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Minus 10x.

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So that's plus 26x minus 18.

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There.

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We're done.

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Let's do another problem.

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Let's do 2x plus y.

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Whoops, some parentheses.

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I'll stay in one color, since I think you understand

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what we're doing.

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Times 3x plus 2y.

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Well, once again, this is the same thing as -- and we could

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just do it in a little different way, a little

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different order.

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But we could distribute it like this.

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We could say that this is 3x times 2x plus y.

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Plus 2y times 2x plus y.

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See what I did?

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I just switched the order this time.

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Just to mix things up.

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This 3x is there.

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This 2y is here.

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And we just distributed it along 2 -- and we just, we

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distributed it 2x plus y along each of these numbers.

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And now we just multiply it out.

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3x times 2x is 6x squared.

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3x times y -- that's 3xy.

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3xy is just another way of saying 3 times x times y.

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Plus, now, 2 times y times 2y times 2x, well, that's 4 y x.

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4 y x.

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2 times 2 times y times x.

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Plus 2y times y.

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Well, that's just 2y squared.

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Now, can we simplify anything here?

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Think about it a little bit.

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Well, it turns out that x y and y are actually the same thing.

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They're just switching the order.

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So you could just rewrite this as 6x squared plus

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7 x y plus 2y squared.

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And we could have just as easily have written it as

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6x squared plus 7y x plus 2y squared.

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I hope I'm not confusing you.

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Let's do one more, real fast.

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Let's do 2x plus 2 squared.

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Well, you might be temptd to just square each of these

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terms, but you've got to be careful because you

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have this x here.

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So it actually turns out that this is equal to 2x

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plus 2 times 2x plus 2.

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Any number squared is just that number times itself.

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So any expression like 2x plus 2 squared, is just that

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expression times itself.

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And now we can just do it as -- this is the same thing

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as 2x times 2x plus 2.

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Plus 2 times 2x plus 2.

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We just multiply everything out.

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2x times 2x, that's 4x squared.

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2x times 2, that's 4x.

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Plus 2 times 2x is 4x again.

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And then 2 times 2, well, that's 4.

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And we're almost there.

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We just can add up these two terms.

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4x squared plus 8x plus 4.

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And we're done.

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I think you're ready now to try some level one multiplying

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expression problems.

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Hope you have fun.