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RC
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Algebra - Example 3

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

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Elyse G.

Cornell University

Farnaz M.

Simon Fraser University

Zachary M.

Hope College

Jared E.

University of Winnipeg

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welcome to our algebra review video on the distributive property. Now, the reason we're covering the distributive property is because it's one that I see a lot of students get caught up with when I use it quickly, and I will often skip algebraic steps simply to shorten the time of the video and help you get through it. But you should definitely go back and make sure you understand how each step works. Algebraic Lee. Otherwise, you'll get caught up in it inside a test, and it won't work out for you. Um, so we're going to consider this in terms of one of the most common equations that we see when we're working with Kidney Matics, which is the first unit of physics? Um, this equation generally looks something like this. It says X is a function of time is equal to your initial position. X not plus your initial velocity V not times the independent. Variable time plus one half times your acceleration times in independent variable time squared. OK, now, when you're looking at this problem and you might say, Okay, what am I gonna do here? How do I solve for this thing? Well, first things first. I'm in physics. Generally, what will happen is we'll move X not over here. It will actually call the left hand side. X of T minus X not equal to a change in X will call that Delta X. Okay, so this is like saying the final exposition minus the initial exposition. Okay. And that's still equal to be not t plus one half A t squared will notice here that the thing that's really crying out for me to use the distributive property is I can pull a t out from the two terms over here, So I have one half the knot, plus one half a t. All of that times t. Okay. Now, the specific place that this is useful from your solving for is if the Delta X is zero. Because if we have Delta X equals zero equals this equation. Thank you. Way of Delta X equals zero. Then we know that this tea right over here one of the solutions for tea is simply zero. Okay, If that's not an option physically, then we know that the only physically reasonable answer is the one inside of here. And so we can very quickly just solve for t using the equation. Zero equals V not plus one half a t. Okay, So by using the distributive property to pull the tea out of these two terms were able to very quickly solve for T. In this case. Now there's other cases that show up like this is well, another place that it shows up that the distributive property is very important is when we're working with forces and we have forces that are pointing in different directions because generally when we try to add those things up, we'll end up with something that looks like this will have forced number one minus forced number two minus forced number three. And that's equal to a negative mass times acceleration, which again you'll learn when we get to talking about forces in a couple units. Now, in this case, say you wanted to solve for acceleration. Okay, you can see how important is toe. Have the sign right on each of the forces. Because if I want to solve for acceleration, I'm gonna have to move this sign over here. So I have a negative one times F one minus f to minus F three is equal to mass times acceleration, and then I'm going to distribute that negative through. On the other hand, I could have pulled a negative out and had a negative one over here and a negative one over here, and they would have eliminated each other. Either way, I'm gonna end up with F two plus F three minus F one equals mass times acceleration. And then I can quickly solve for a So these air just two very brief examples of how I would use the distributive property without really saying Okay, guys, use the distributive property to solve for this equation. So make sure that you're able to use this property, uh, efficiently and that you're able to see it happen when I use it in a problem.

RC
University of North Carolina at Chapel Hill
Top Physics 101 Mechanics Educators
Elyse G.

Cornell University

Farnaz M.

Simon Fraser University

Zachary M.

Hope College

Jared E.

University of Winnipeg