>> Math is cool and you can do it.
>> Alright, we are going to go over evaluating algebraic expressions.
These will be basic ones.
There will be no negative numbers.
So, to evaluate an expression replace each variable with a specified number,
so you have to be told what number to plug in for a variable
and then use the order of operation to simplify.
So, here are a couple of examples, evaluate each expression
if x equals 2, n equals 1, and y equals 5.
So, let us do number 1, 4y squared minus xn.
My first suggestion is any time you have something with exponents
that you write it as multiplication first.
So that is what I am going to do first for number 1.
I am going to write y squared as y times y, so I have 4 times y, times y,
and remember xn means x times n. The reason I am writing this
as y times y is so you realize it doesn't mean 4y times 4y.
The base is just the y, so it is 4 times y squared.
So, now we could plug in the values of y, x, and n, so we have 4 times 5 times 5 minus x is 2,
so I will put in 2 for x, and n is 1.
And now we are going to do our order of operations.
So, we could do our little underlining method, so I have 4 times 5 times 5, that is 100,
minus 2 times 1 is 2, so my final answer is 98.
So the value of this expression is 98 when x equals 2, n equals 1, and y equals 5.
Now, you might not have all the variables in a particular expression.
For instance in number 2, there is a y and there is an x
but there is no n. We do exactly the same thing.
I am going to start off by writing x squared as x times x, plus 1.
Now this is a suggestion, you don't have to do that.
Alright, so y, we are going to replace y with a 5, and we are going to replace x with 2,
and what do I have here, 5 over -- now, in the bottom, I have got 4 plus 1.
And now I have to simplify the denominator still, I am going to run out of room here,
I am going to have to move up a little.
So, we have 5 over 5, and then 5 divided by 5 is 1, so the final answer here will simply be 1.
Okay, here is a couple more to try, so for the first one number 3, we are going to replace y
with 5, x with 2, and n with 1, alright.
So, for five halves, you could either leave that as five halves or you could write
that as a decimal which would be 2.5 or you can write as two and a half.
So, there are different ways you might deal with this 5 divided by 2.
I am going to go ahead and write it as two and a half, so I am just changing it
to a mixed number, minus and then 2 times 1.
Notice what I am doing is, I am just doing division and multiplication as it occurs
from left to right, I do my subtraction last.
So we have two and a half minus 2 and so my answer is one half.
Now, if you had written it as 2.5 minus 2, you might have written your answer as 0.5.
And if you would have left it as five halves and got a common denominator for two of four halves,
you would have probably written it as one half.
So, those are really all of the same answer,
and three different people may do it three different ways.
Alright, let's go on to number 4.
So, I first have to replace the variables with the correct substitutions, so for n I am going
to put in 1, and for y I am putting in 5.
And now again remember your order of operations, you do not do the 3 plus 2,
we do inside parentheses first, so you copy up to that point.
And now what, we have done inside parentheses, right?
Now we have to do exponents, and my suggestion which you do not have to take,
you can write 2 times 36 or you could write 2 times 6, times 6 first.
In any case at your next step you will get 72 because next you do your multiplication.
Do not add until the end, so my final answer here is going to be 75.
[ Pause ]
>> So, here are a couple more problems, alright.
So for number 5, there are no parentheses, next thing, I am sorry.
So here are a couple more problems, so we are going to replace the variables
with a particular numbers, but when you have exponents, I think it is easier
to first write the exponents what they mean before replacing the variables.
So if we do that, I could first write this as y times y,
x times y times y minus x times x. Alright, now we could replace it.
So, it is up to you whether you want to replace it before then or not.
So, I am going to replace x with a 2, y with a 5, and x with a 2.
So, what do we have here, we have got 10 times 5 or 50 minus 2 times 2 is 4, and that is 46.
Here is what it would look like if you replace it first.
So, starting out with the same problem, xy squared minus x squared, I am replacing again 2
for x. I could put it in the 2 for x, right?
And then I have to be careful 2 is not being squared.
I am going to put in 5 for y, so you could put the 5 in parentheses,
or you could write it as just 5 squared.
You do have to be careful though if when we do work with negative numbers,
you must put negative numbers in parentheses, if you are putting them
for a base with something with the exponent.
And then we would have minus and then of course I would be putting in the 2 for the x as well.
So you would either write it like this or if you want, you could put parentheses around the 5
or each of the two, so that is really up to you.
So, some people might write it like this.
And in fact if you want you could also write the two in parentheses, that is all up to you.
Okay, so now I have to do my order of operations first so within this first term,
I am going to have to do the 5 squared, so I would have 2 times 25
and over here my two squared is 4, so notice I would still end up with 50 minus 4, which is 46.
People make less mistakes, fewer mistakes,
I believe when they first rewrite what something needs
to be squared before replacing the variable.
Alright, let us do the second problem over here, n plus y over n plus x. So,
I am going to replace n with a 1, and y with a 5, and in the denominator I am going
to replace n with 1, and x with a 2.
Now, you cannot cancel, remember, you need to simplify the numerator
and simplify the denominator first as if they are in parentheses.
So, 1 plus 5 is 6, 1 plus 2 is 3, and this reduces actually,
6 divided by 3 to just the number 2.
I hope you learned something, remember math is cool.