Combining Like Terms
Uploaded by MuchoMath on 01.03.2009
Transcript:
>> Professor Perez: Hey!
This is Professor Perez again.
Today, we're going to work on combining like terms.
Oh what fun!
And of course, we've got to get Charlie out.
He better be ready to go!
Charlie, you ready to go?
>> Charlie: Yeah!
>> Professor Perez: We're doing combining like terms.
>> Charlie: Woo hoo...
>> Professor Perez: Oh, you think that's fun, huh?
Well it better be!
All right, Charlie, here's our first problem, let's make it a tough one.
Right there!
You better not miss this.
All right, Charlie, what's 1 plus 1?
>> Charlie: 2.
>> Professor Perez: Uh-huh, you got that one right.
Okay, let's step it up a bit.
Now, Charlie, what's this one?
x plus x?
>> Charlie: x squared!
>> Professor Perez: No it is x squared if you'd like to repeat this class, Charlie!
It's like 1 x plus another x is how many x's, Charlie?
>> Charlie: 2x.
>> Professor Perez: That's right.
It's 2x. All right, Charlie, okay.
Let's see if you can recover.
Try this one.
>> Charlie: x squared.
>> Professor Perez: Uh-huh, now you know the answer, huh!
Yeah, that is x squared.
All right, Charlie.
Okay, Charlie, what's 2 plus 3?
>> Charlie: 5.
>> Professor Perez: That's right.
Okay, be careful.
Now, what's 2x's plus 3 more x's?
>> Charlie: 5 x's.
>> Professor Perez: That's right, 5 x's.
Yeah, you can't miss that one.
Now don't get scared, just relax.
Here we go, Charlie.
What's 2 sevenths plus 3 more sevenths?
>> Charlie: 5 sevenths.
>> Professor Perez: That's right.
All of those problems just require that you have the ability
to add 2 plus 3...without a calculator.
All right, Charlie, here we go.
5 plus 3 subtract 2.
Remember, you must work left to right according to the Order of Operations.
And so what's 5 plus 3?
>> Charlie: 8.
>> Professor Perez: Subtract 2?
>> Charlie: 6.
>> Professor Perez: Very nice, there Charlie.
That's right.
It's not 0, unless you'd like to repeat this class...uh-huh...with him!
All right, Charlie, here we go.
Same problem, but it's elevenths.
What's 5 elevenths plus 3 more elevenths take away 2
of your elevenths, what do you get, Charlie?
>> Charlie: 6 elevenths.
>> Professor Perez: That's right.
6 elevenths, same problem.
Now don't get scared, Charlie.
Don't miss this one.
5 apples plus 3 more apples take away 2 of your apples gives you how many apples, Charlie?
>> Charlie: 6 apples.
>> Professor Perez: 6 apples.
Very nice there.
So, okay, now that we're warmed up, let's get to the real problems!
2x plus 3x plus 2 plus 4.
Oh what fun.
Now, remember, Order of Operations says we have to work left to right.
So, what's 2x plus 3x, Charlie?
>> Charlie: 5x.
>> Professor Perez: 5x.
That's right.
And so notice, 2x plus 3x is 5x, and now,
we're going to do the 2 plus 4, which is what, Charlie?
>> Charlie: 6.
>> Professor Perez: 6.
And that is our answer here.
Now, notice, Order of Operations says we're supposed to work left to right.
So, we were supposed to do 2x plus 3x which is 5x and then add the 2.
But, we did not add the 2 to the 5x because we can't do that.
So, one thing to remember, if everything is being added together,
we can use the associative property and commutative property for addition to show
that we can add in any order we want, right?
Okay, let's apply that to this problem here.
Now, look at this, Charlie.
What are the like terms?
>> Charlie: 2x and 3x.
>> Professor Perez: Okay, so we'll add those together and we'll bring down our work.
Now, Order of Operations says you're supposed to work left to right, correct?
But we cannot do 5x subtract 2, so what we have to do is visualize
that subtract as being adding a negative 2.
And remember, if everything is being added together, you can go in any order you want.
So, in this case, now Charlie, notice we can add the negative 2 plus 4 which is what, Charlie?
>> Charlie: 2.
>> Professor Perez: 2.
And that is the correct answer.
So, those two little middle steps, sometimes people don't like to write them out,
they just do it mentally, which is okay.
But as long as you understand what you're doing, you're fine.
Write out the steps, and that will help you understand
and approve your combining like terms ability.
So here we go, Charlie.
5a subtract 3 subtract 3a.
Remember, Order of Operations says you're supposed to work left to right,
but if we visualize everything being added, in this case adding a negative 3
and adding a negative 3a, it's the same problem, but now,
since everything is being added, we can add in any order we want.
And what's 5a plus a negative 3a, Charlie?
>> Charlie: 2a.
>> Professor Perez: 2a.
And don't forget to bring down your plus a negative 3.
Now, our final answer is what, Charlie?
>> Charlie: 2a subtract 3.
>> Professor Perez: That's right.
2a subtract 3.
And again, if you can do the problem with skipping those two middle steps, that's fine.
But as long as you realize what you're actually doing.
Okay, so let's step it up a bit.
Don't get scared with this one, Charlie.
Now, here, we can't work left to right, but we can visualize everything here being added
by writing it as adding a negative 5, plus adding a negative 3x, and adding a negative 2,
and adding a negative x. Now we can go in any order so let's define our like terms.
We have all those x's there, Charlie, and then we have those numbers.
Now, Charlie, what's 7x plus a negative 3x?
>> Charlie: 4x.
>> Professor Perez: Subtract x?
>> Charlie: 3x.
>> Professor Perez: Is 3x.
Very nice there, Charlie.
Now, what's a negative 5 plus a negative 2?
>> Charlie: Negative 7.
>> Professor Perez: That's right.
And our final answer is 3x subtract 7
because adding a negative number is the same as subtracting the opposite.
We should know how to do that.
There's our final answer.
Okay, and again, some of you can go straight from the top to the bottom.
That's good, but I hope you can do it without your calculator.
All right, Charlie, let's do another one.
Oh what fun!
Don't get scared.
Here we go, Charlie, we have all of these subtractions in there,
so let's change our subtractions to adding the negative quantities here.
Just like this.
Okay. Now, let's define our like terms.
First we'll start with the a's, Charlie.
Notice, we have a 2a, a 1a, and a negative 4a.
And with our b's, we have a negative b, plus a negative 8b, plus a 3b.
And we have that negative 4 at the end.
Okay, Charlie, so, 2a plus a is what, Charlie?
>> Charlie: 3a.
>> Professor Perez: Subtract 4a?
>> Charlie: Negative a.
>> Professor Perez: Negative a. Let me let you know that you don't have to put the parenthesis
around the negative a. I'm just doing it for presentation.
So, we have a negative a. Now, let's combine our b's.
What's a negative b plus a negative 8b, Charlie?
>> Charlie: Negative 9b.
>> Professor Perez: Plus a 3b?
>> Charlie: Negative 6b.
>> Professor Perez: Negative 6b.
Very nice.
And bring down your negative 4.
And all we have to do is bring down our work.
Take off the parenthesis.
Negative a subtract 6b subtract 4.
And there it is.
So that's our lecture on combining like terms.
Oh what fun!
We'll see you again soon!
This is Professor Perez again.
Today, we're going to work on combining like terms.
Oh what fun!
And of course, we've got to get Charlie out.
He better be ready to go!
Charlie, you ready to go?
>> Charlie: Yeah!
>> Professor Perez: We're doing combining like terms.
>> Charlie: Woo hoo...
>> Professor Perez: Oh, you think that's fun, huh?
Well it better be!
All right, Charlie, here's our first problem, let's make it a tough one.
Right there!
You better not miss this.
All right, Charlie, what's 1 plus 1?
>> Charlie: 2.
>> Professor Perez: Uh-huh, you got that one right.
Okay, let's step it up a bit.
Now, Charlie, what's this one?
x plus x?
>> Charlie: x squared!
>> Professor Perez: No it is x squared if you'd like to repeat this class, Charlie!
It's like 1 x plus another x is how many x's, Charlie?
>> Charlie: 2x.
>> Professor Perez: That's right.
It's 2x. All right, Charlie, okay.
Let's see if you can recover.
Try this one.
>> Charlie: x squared.
>> Professor Perez: Uh-huh, now you know the answer, huh!
Yeah, that is x squared.
All right, Charlie.
Okay, Charlie, what's 2 plus 3?
>> Charlie: 5.
>> Professor Perez: That's right.
Okay, be careful.
Now, what's 2x's plus 3 more x's?
>> Charlie: 5 x's.
>> Professor Perez: That's right, 5 x's.
Yeah, you can't miss that one.
Now don't get scared, just relax.
Here we go, Charlie.
What's 2 sevenths plus 3 more sevenths?
>> Charlie: 5 sevenths.
>> Professor Perez: That's right.
All of those problems just require that you have the ability
to add 2 plus 3...without a calculator.
All right, Charlie, here we go.
5 plus 3 subtract 2.
Remember, you must work left to right according to the Order of Operations.
And so what's 5 plus 3?
>> Charlie: 8.
>> Professor Perez: Subtract 2?
>> Charlie: 6.
>> Professor Perez: Very nice, there Charlie.
That's right.
It's not 0, unless you'd like to repeat this class...uh-huh...with him!
All right, Charlie, here we go.
Same problem, but it's elevenths.
What's 5 elevenths plus 3 more elevenths take away 2
of your elevenths, what do you get, Charlie?
>> Charlie: 6 elevenths.
>> Professor Perez: That's right.
6 elevenths, same problem.
Now don't get scared, Charlie.
Don't miss this one.
5 apples plus 3 more apples take away 2 of your apples gives you how many apples, Charlie?
>> Charlie: 6 apples.
>> Professor Perez: 6 apples.
Very nice there.
So, okay, now that we're warmed up, let's get to the real problems!
2x plus 3x plus 2 plus 4.
Oh what fun.
Now, remember, Order of Operations says we have to work left to right.
So, what's 2x plus 3x, Charlie?
>> Charlie: 5x.
>> Professor Perez: 5x.
That's right.
And so notice, 2x plus 3x is 5x, and now,
we're going to do the 2 plus 4, which is what, Charlie?
>> Charlie: 6.
>> Professor Perez: 6.
And that is our answer here.
Now, notice, Order of Operations says we're supposed to work left to right.
So, we were supposed to do 2x plus 3x which is 5x and then add the 2.
But, we did not add the 2 to the 5x because we can't do that.
So, one thing to remember, if everything is being added together,
we can use the associative property and commutative property for addition to show
that we can add in any order we want, right?
Okay, let's apply that to this problem here.
Now, look at this, Charlie.
What are the like terms?
>> Charlie: 2x and 3x.
>> Professor Perez: Okay, so we'll add those together and we'll bring down our work.
Now, Order of Operations says you're supposed to work left to right, correct?
But we cannot do 5x subtract 2, so what we have to do is visualize
that subtract as being adding a negative 2.
And remember, if everything is being added together, you can go in any order you want.
So, in this case, now Charlie, notice we can add the negative 2 plus 4 which is what, Charlie?
>> Charlie: 2.
>> Professor Perez: 2.
And that is the correct answer.
So, those two little middle steps, sometimes people don't like to write them out,
they just do it mentally, which is okay.
But as long as you understand what you're doing, you're fine.
Write out the steps, and that will help you understand
and approve your combining like terms ability.
So here we go, Charlie.
5a subtract 3 subtract 3a.
Remember, Order of Operations says you're supposed to work left to right,
but if we visualize everything being added, in this case adding a negative 3
and adding a negative 3a, it's the same problem, but now,
since everything is being added, we can add in any order we want.
And what's 5a plus a negative 3a, Charlie?
>> Charlie: 2a.
>> Professor Perez: 2a.
And don't forget to bring down your plus a negative 3.
Now, our final answer is what, Charlie?
>> Charlie: 2a subtract 3.
>> Professor Perez: That's right.
2a subtract 3.
And again, if you can do the problem with skipping those two middle steps, that's fine.
But as long as you realize what you're actually doing.
Okay, so let's step it up a bit.
Don't get scared with this one, Charlie.
Now, here, we can't work left to right, but we can visualize everything here being added
by writing it as adding a negative 5, plus adding a negative 3x, and adding a negative 2,
and adding a negative x. Now we can go in any order so let's define our like terms.
We have all those x's there, Charlie, and then we have those numbers.
Now, Charlie, what's 7x plus a negative 3x?
>> Charlie: 4x.
>> Professor Perez: Subtract x?
>> Charlie: 3x.
>> Professor Perez: Is 3x.
Very nice there, Charlie.
Now, what's a negative 5 plus a negative 2?
>> Charlie: Negative 7.
>> Professor Perez: That's right.
And our final answer is 3x subtract 7
because adding a negative number is the same as subtracting the opposite.
We should know how to do that.
There's our final answer.
Okay, and again, some of you can go straight from the top to the bottom.
That's good, but I hope you can do it without your calculator.
All right, Charlie, let's do another one.
Oh what fun!
Don't get scared.
Here we go, Charlie, we have all of these subtractions in there,
so let's change our subtractions to adding the negative quantities here.
Just like this.
Okay. Now, let's define our like terms.
First we'll start with the a's, Charlie.
Notice, we have a 2a, a 1a, and a negative 4a.
And with our b's, we have a negative b, plus a negative 8b, plus a 3b.
And we have that negative 4 at the end.
Okay, Charlie, so, 2a plus a is what, Charlie?
>> Charlie: 3a.
>> Professor Perez: Subtract 4a?
>> Charlie: Negative a.
>> Professor Perez: Negative a. Let me let you know that you don't have to put the parenthesis
around the negative a. I'm just doing it for presentation.
So, we have a negative a. Now, let's combine our b's.
What's a negative b plus a negative 8b, Charlie?
>> Charlie: Negative 9b.
>> Professor Perez: Plus a 3b?
>> Charlie: Negative 6b.
>> Professor Perez: Negative 6b.
Very nice.
And bring down your negative 4.
And all we have to do is bring down our work.
Take off the parenthesis.
Negative a subtract 6b subtract 4.
And there it is.
So that's our lecture on combining like terms.
Oh what fun!
We'll see you again soon!