Hey guys!
Welcome to this video on adding and subtracting with Exponents.
To start off, just so that we are all on the same page, I'm going to define exponents as
well as a few other things so that moving forward, hopefully, there won't be as much confusion.
So, I'll start with the base (or variable base in this case).
The base is the number that is being raised to the power of something,
and that number it is being raised by is called the exponent.
Now, what an exponent represents is how many times that base is being multiplied by itself.
So, in this case "x", our base, is being multiplied by itself twice( x*x).
The number out in front of the base or variable is called the coefficient.
Hopefully, now, moving forward you will be able to better follow what I'm talking about as I reference these terms.
Now, Let's take a look at a problem.
5x^3+9x^3 Alright so in order for us to simplify this
we have to look for two things.
One, are our bases (or variables) the same; and two, are our exponents the same
Both things have to be true in order for us to add these two terms together.
This same process of adding and subtracting with exponents is also called combining like
terms, which may sound more familiar to you.
Okay, so looking back at our problem we can see that our bases are the same, and our exponents are the same.
Which means we have two like terms that can be combined together.
So, to actually combine them here is what you do:
Add the coefficients together, and leave your base and exponent the same.
In this problem our coefficients are 5 and 9.
5 + 9 is equal to 14.
So, leaving our base and exponent alone we get 14x3.
Remember, to add or subtract numbers that have exponents you must first make sure that
the base and exponent of the two terms you are trying to add or subtract are the same.
If they are the same, then all you have to do is add together their coefficients
and keep the base and exponent the same.
Let's look at another example.
2x^2 + 5 4x^3 + 7x^3 x^2 Alright, so in this example some of the terms
have different exponents.
So, we need to identify all of our terms that can be combined together in order to simplify this expression.
Starting with 2x^2, are there any other terms with an identical base and exponent Yes,
our -x^2.
5 is on it's own, and 4x^3 + 7x^3 share identical base and exponents.
We know that to combine our like terms together, all we need to do is add together the coefficients
of the corresponding like terms.
So, here is how we can do that.
Since, we are adding the coefficients of 2x2 and x2 together, and all other like terms,
we can rewrite this expression to help us follow our work.
(7-4)x^3 + (2-1)x^2 +5 Now, the reason I brought my term with a 3
in the exponent to the front is, because in the standard form of a polynomial equations
you always bring your term with the highest number in the exponent to the front (or to the left).
Now, when we add our coefficients together we get:
3x^3 + x^2 + 5 At this point all of our like terms have been
combined, and there is no further simplification that we can do.
So, we are done.
I hope this video was helpful.
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See you next time!