Concepts then Algebra i Unit Expressions

Explaining the Concepts. Explain how to subtract polynomials.

All right. So here we are asked to describe what equivalent algebraic expressions are an equivalent just means equal we want. If we were to come up with the solution for both of these expressions, they would have the same outcome. They would have the same product or some, and so if we let's just start off with an example. So let's say we have eight X Plus four.

We want to make an equivalent expression here. Well, from the properties that learned in this chapter, such as the Community of property of Addition. It tells us that no matter what order we add, two numbers in it's still gonna have the same some. So four plus eight X would also be an equivalent expression. Another example.

Maybe. Let's use a little more if we have three X Plus seven plus for why, right? If we used the associative property, it says that no matter what order you add, three numbers in it still is going to have the same some. So we had three x plus seven plus four y. That's still going to be an equivalent expression, so pretty much what a equivalent outbreak expression as something that you can come up with the same solution or it means the same thing pretty much. They go.

Vessel in an algebraic expression. We have variables involved, but in New Miracle, expect expressions. We only have, uh, numbers and operations symbol..

So this question here is asking us to multiply it out and simplify. So what we're gonna do is we're going to take this square root and put it in tow exponents for him because I feel that that's easier way to go about solving this problem. So the first thing we do is we know that the square root of ax is the same as acts to the 1/2. And then I have this multiplied times in parentheses, another square root, and we'll put that one and exponents warm as well. And so now when we're multiplying this out, remember what I have in front here.

When I have parentheses, I have to distribute to each one of the terms here. So the first thing we do is we multiply X to the 1/2 times and X. And then remember, we have this minus sign and then that'll be X to the 1/2. We'll put this in parentheses just to make it a little bit more clear times and acts to the 1/2. So remember when you're multiplying, uh, numbers with the same base.

So the base here is acts. We add the exponents aware of this is an axe to the one. And in order to add fractions, I have tohave the same denominator. So to turn a one into a denominator of two, I'm just gonna multiply the top and bottom times a two. And then I get to over two for this.

So when I'm adding these exponents here, I haven't acts to the 1/2 plus a two over two. And then I'm subtracting, And here already the denominator is the same, so I can just add those. So I have a 1/2 plus a 1/2 which is just one. So I'll leave that off there and then completing this here I get X to the three halves minus X. You can also write this as the square root of acts to the third, because this, too, is in here assumed in here minus acts.

So both of these answers are correct..

Okay, so let's say we have to rational expressions and we're multiplying them to multiply together. We just multiplied through our enumerators. So that's a C and R denominators, so that's Bt..