Level 1 multiplying expressions

Algebra

Polynomials

Multiplying monomials, binomials and polynomials in general

Multiplying Monomials
Dividing Monomials
Multiplying and Dividing Monomials 1
Multiplying and Dividing Monomials 2
Multiplying and Dividing Monomials 3
Monomial Greatest Common Factor
Factoring and the Distributive Property
Factoring and the Distributive Property 2
Factoring and the Distributive Property 3
Multiplying Binomials with Radicals
Multiplication of Polynomials
Multiplying Binomials
Multiplying Polynomials1
Multiplying Polynomials 2
Square a Binomial
Special Products of Binomials
Special Polynomials Products 1
Factor polynomials using the GCF
Special Products of Polynomials 1
Special Products of Polynomials 2
Multiplying expressions 0.5
Factoring linear binomials
Multiplying expressions 1
Multiplying Monomials by Polynomials
Multiplying Polynomials
Multiplying Polynomials 3
More multiplying polynomials
Multiplying polynomials

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Level 1 multiplying expressions

Level 1 multiplying expressions (Ax+By)(Ax+By)

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Level 1 multiplying expressions

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Welcome to the presentation on multiplying expressions.
Let's get started.
So if I were to ask you what x plus two times, let me use a
different color, times x plus three 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 three, you
know that that's just a x plus, you could say a three, or
another way to say that would be three a, right?
But as you see, all we did is distribute it, this a times three.
All we did is distribute the a times the x and the three.
Well, we're going to do the same thing here, but instead
of a we have x plus two.
So let's do that.
So this would be -- let me switch to green -- we get x
plus two, and since I'm using green, I'm just going
to stay with green.
x plus two, let me switch to orange.
x plus two times x plus x plus two times three.
Does that make sense?
If that looks a little confusing, just pretend
like that x plus two 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 two -- well, that's twox.
So we did this left-hand side already.
Now we do this right-hand side.
What's three times x?
Well that's threex.
What's three times two?
Well, that's six.
And now we're almost done.
We could say, oh, we have a twox here and a threex here, we can
simplify and add those together.
And we know that that equals x squared.
twox plus threex is equal to fivex.
x squared plus fivex plus six.
So all we did, there's really nothing new to learn here.
We just distributed the x plus two times each term of x plus three.
And we got the second step.
And then we distributed this x times x plus two, and this three
times x plus two, and simplify.
Let's do a couple of problems.
And hopefully it'll hit the point home.
Let's say I had fivex plus nine times fourx minus two.
Once again, that equals fivex plus nine.
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 fivex plus nine times fourx.
And then plus, fivex plus nine times minus two.
That minus two is here and this fourx is here.
And now we just multiply it out.
fivex times fourx is twentyx squared.
Hope that makes sense to you; let me write it
down in this corner.
fivex times fourx is the same thing as five times four times x times x.
That equals twentyx squared.
Hopefully that makes sense to you.
So, going back to the problem.
fivex times fourx is twentyx squared plus nine times fourx is thirty-sixx.
Plus minus two times fivex.
So that's minus tenx.
And then nine times negative two, well, that's minus eighteen.
And we're almost done.
So we get twentyx squared.
And we have thirty-sixx.
Minus tenx.
So that's plus twenty-sixx minus eighteen.
There.
We're done.
Let's do another problem.
Let's do twox plus y.
Whoops, some parentheses.
I'll stay in one color, since I think you understand
what we're doing.
Times threex plus twoy.
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 threex times twox plus y.
Plus twoy times twox plus y.
See what I did?
I just switched the order this time.
Just to mix things up.
This threex is there.
This twoy is here.
And we just distributed it along two -- and we just, we
distributed it twox plus y along each of these numbers.
And now we just multiply it out.
threex times twox is sixx squared.
threex times y -- that's threexy.
threexy is just another way of saying three times x times y.
Plus, now, two times y times twoy times twox, well, that's four y x.
four y x.
two times two times y times x.
Plus twoy times y.
Well, that's just twoy 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 sixx squared plus
seven x y plus twoy squared.
And we could have just as easily have written it as
sixx squared plus seveny x plus twoy squared.
I hope I'm not confusing you.
Let's do one more, real fast.
Let's do twox plus two 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 twox
plus two times twox plus two.
Any number squared is just that number times itself.
So any expression like twox plus two squared, is just that
expression times itself.
And now we can just do it as -- this is the same thing
as twox times twox plus two.
Plus two times twox plus two.
We just multiply everything out.
twox times twox, that's fourx squared.
twox times two, that's fourx.
Plus two times twox is fourx again.
And then two times two, well, that's four.
And we're almost there.
We just can add up these two terms.
fourx squared plus eightx plus four.
And we're done.
I think you're ready now to try some level one multiplying
expression problems.
Hope you have fun.

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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

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