Let's look at a few examples where we practice the distributive property.
Here's our first example.
We have the quantity four plus k, minus the quantity one, plus three k.
Now right off the bat it doesn't appear to have a distributive property, cause we don't
really see a clear cut number outside one of our parenthesis like a three or something
like that, that would need to be distributed.
But in fact there is ah, it's just a little hard to spot.
Uhm, this minus sign right here, is actually, you could think of it as plus negative one.
You could think, of minus, as plus negative one, times the quantity one plus three k.
So the distributive property is applicable here, we would need to distribute this negative
throughout the last two terms.
The first two terms do not have a distributive property, but the second terms do.
So this would give us four plus k, since there's no distributive property, we can just drop
the parenthesis.
Then we can say, minus one, minus three k, cause you have to remember when you distribute
this negative, the negative goes in for both terms here.
Now just as a side note, not to get off on a tangent here, if this plus sign had been
a minus, then a minus a negative, would've have turned this into a plus.
It wasn't, but I'm just saying if it was, a negative, a negative, would have made it
positive.
But that's not what we have.
So anyway we're almost done, this is definitely the right next step, so from here we have
to do a, simplify our answer.
I see like terms of the four and the negative one, the two constants.
Four minus one gives me three.
And k minus three k is like terms so both of those are like terms so that would yield
minus two k.
So this would be our final answer after distributing the negative and combining like terms.
Alright ah, here we have a distributive property with three terms.
We have negative seven, times the quantity two, plus three a, minus b.
So what we'll do is we'll take this negative seven, and we'll distribute it to the first,
the second, and the third term.
That's totally allowed, you are totally allowed to do that.
So we would get minus fourteen, that's negative seven times two.
Ah, and then, negative seven times three a, would give us negative twenty-one a, so we
would have minus twenty-one a.
And then, here's a very common occurrence as well, we have a negative times a negative,
which will actually turn into a plus.
So we'll have negative seven times negative b, makes positive seven b.
So we'll add seven b.
Uhm, you'll look at this guy see if there's any like terms, there's not.
So this is our final answer for this problem.
Alright, uhm, here's our last example.
And this one's a little bit more challenging.
We actually have ah, two different distributive properties that I see, but one is nested within
inside the other one.
So one that I see is the six, times all of these things that are being added or subtracted.
Ah, but then I also see, here on the inside, I've got two times the quantity y minus five.
We will also need to distribute this two.
So what do we do?
Well I usually like to work from the inside out.
I think that's a little safer.
So let's worry about this, ah, what's inside the largest brackets, and then we'll take
care of the six when we're done.
So we have x minus two times the quantity y, minus five.
Let's go ahead and distribute this two right here, and let's simplify that before we go
any farther.
So we'll six times the quantity x.
Then we'll have minus two y, because we're distributing the negative two to the y.
And negative two times negative five, makes plus ten.
Okay, so notice, once we've applied the distributive property inside the brackets, the parenthesis
on the inside are gone.
Right, we've applied the distributive property.
Alright, so the last step would be to take care of this distributive property, where
we multiply the six times the x, the two y, and the ten.
Okay, six times x, is six x.
Ah, the six times negative two y would be minus twelve y.
And the six times ten, would be sixty.
Look for any like terms, I don't think there are any, so I think we're done with this one.
Alright now, I'm not going to actually go very far with this next example, this will
be, this will actually come later in the course, but I feel kind of obligated to go ahead and
mention it right now.
If you have a quantity, I'll just make up a number here, let's say four, times a quantity
x, plus two, but this quantity is actually squared, or cubed, let's say cubed.
Well, we'll say squared.
Let's say x plus one, quantity squared.
If you have a term times a sum or difference, but this guy's raised to a power higher than
one, like squared, or cubed, etcetera, then you cannot, you cannot, use the distributive
property.
A lot of students that I have will desperately want to use the distributive property, because
it looks like the right thing to do, but you cannot distribute the four to the x, and the
four to the one.
And the reason again, is because this is square.
So just remember if you have an exponent up there that basically locks it down from being
able to distribute a number inside those parenthesis.
Now that leads to a question we're not going to answer in this video.
Now the question would be, well then Devin what do we do then?
That's going to come later in the course, I'm not going to take time to talk about that
right now.
Just for now, know that you are not allowed to distribute if this exponent is anything
larger than one.