Welcome to the presentation on multiplying expressions.
Let's get started.
So if I were to ask you what x plus 2 times, let me use a
different color, times x plus 3 equals, at first you'd be like,
huh, that's a little strange.
But it turns out that you actually already know
how to do this problem.
And it's just the distributive property.
Because, if I just had -- let me write a different problem
here -- if I just wrote a let me just make it clear, this is
a separate problem -- if I just wrote a times x plus 3, you
know that that's just a x plus, you could say a 3, or
another way to say that would be 3a, right?
But as you see, all we did is distribute it, this a times 3.
All we did is distribute the a times the x and the 3.
Well, we're going to do the same thing here, but instead
of a we have x plus 2.
So let's do that.
So this would be -- let me switch to green -- we get x
plus 2, and since I'm using green, I'm just going
to stay with green.
x plus 2, let me switch to orange.
x plus 2 times x plus x plus 2 times 3.
Does that make sense?
If that looks a little confusing, just pretend
like that x plus 2 is the a in this example.
And all we did is, we distributed it across
that x plus three.
And now it becomes a pretty straightforward problem.
What is -- we do distribution again with each part
of this problem.
So, let me stay in orange.
What is x times x?
Well that's x squared.
And then x times 2 -- well, that's 2x.
So we did this left-hand side already.
Now we do this right-hand side.
What's 3 times x?
Well that's 3x.
What's 3 times 2?
Well, that's 6.
And now we're almost done.
We could say, oh, we have a 2x here and a 3x here, we can
simplify and add those together.
And we know that that equals x squared.
2x plus 3x is equal to 5x.
x squared plus 5x plus 6.
So all we did, there's really nothing new to learn here.
We just distributed the x plus 2 times each term of x plus 3.
And we got the second step.
And then we distributed this x times x plus 2, and this 3
times x plus 2, and simplify.
Let's do a couple of problems.
And hopefully it'll hit the point home.
Let's say I had 5x plus 9 times 4x minus 2.
Once again, that equals 5x plus 9.
I'm just distributing it.
I want to stay in my color that I'm using, so that's why I'm
just writing it out like this.
That equals 5x plus 9 times 4x.
And then plus, 5x plus 9 times minus 2.
That minus 2 is here and this 4x is here.
And now we just multiply it out.
5x times 4x is 20x squared.
Hope that makes sense to you; let me write it
down in this corner.
5x times 4x is the same thing as 5 times 4 times x times x.
That equals 20x squared.
Hopefully that makes sense to you.
So, going back to the problem.
5x times 4x is 20x squared plus 9 times 4x is 36x.
Plus minus 2 times 5x.
So that's minus 10x.
And then 9 times negative 2, well, that's minus 18.
And we're almost done.
So we get 20x squared.
And we have 36x.
Minus 10x.
So that's plus 26x minus 18.
There.
We're done.
Let's do another problem.
Let's do 2x plus y.
Whoops, some parentheses.
I'll stay in one color, since I think you understand
what we're doing.
Times 3x plus 2y.
Well, once again, this is the same thing as -- and we could
just do it in a little different way, a little
different order.
But we could distribute it like this.
We could say that this is 3x times 2x plus y.
Plus 2y times 2x plus y.
See what I did?
I just switched the order this time.
Just to mix things up.
This 3x is there.
This 2y is here.
And we just distributed it along 2 -- and we just, we
distributed it 2x plus y along each of these numbers.
And now we just multiply it out.
3x times 2x is 6x squared.
3x times y -- that's 3xy.
3xy is just another way of saying 3 times x times y.
Plus, now, 2 times y times 2y times 2x, well, that's 4 y x.
4 y x.
2 times 2 times y times x.
Plus 2y times y.
Well, that's just 2y squared.
Now, can we simplify anything here?
Think about it a little bit.
Well, it turns out that x y and y are actually the same thing.
They're just switching the order.
So you could just rewrite this as 6x squared plus
7 x y plus 2y squared.
And we could have just as easily have written it as
6x squared plus 7y x plus 2y squared.
I hope I'm not confusing you.
Let's do one more, real fast.
Let's do 2x plus 2 squared.
Well, you might be temptd to just square each of these
terms, but you've got to be careful because you
have this x here.
So it actually turns out that this is equal to 2x
plus 2 times 2x plus 2.
Any number squared is just that number times itself.
So any expression like 2x plus 2 squared, is just that
expression times itself.
And now we can just do it as -- this is the same thing
as 2x times 2x plus 2.
Plus 2 times 2x plus 2.
We just multiply everything out.
2x times 2x, that's 4x squared.
2x times 2, that's 4x.
Plus 2 times 2x is 4x again.
And then 2 times 2, well, that's 4.
And we're almost there.
We just can add up these two terms.
4x squared plus 8x plus 4.
And we're done.
I think you're ready now to try some level one multiplying
expression problems.
Hope you have fun.