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SAT (Fall 2023)

Course: SAT (Fall 2023) > Unit 10

Lesson 2: Passport to advanced mathematics

Operations with polynomials — Basic example

Watch Sal work through a basic Operations with polynomials problem.

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Video transcript

- [Instructor] Which of the following is equivalent to all of this stuff right over here. One over 88, or 1/88, y to the 100 plus one, minus this entire expression, 1/44 y to the 100 minus 1/2. So let me just rewrite it. So this part right over here, this is going to just be one over 88 y, let me make sure it looks clear, y to the 100th power plus one, and then we're gonna subtract all of this. So one way to think about it is we could distribute this negative sign, so it's gonna be, it's going to be negative, one way you could think about it is negative one, negative one times all of this business. So it's gonna be minus one over 44 y to the 100th, and then a negative, remember, we're gonna distribute it, so negative one times negative 1/2 is going to be plus, plus 1/2. Now, let's see what we can do to further simplify it. So this is 1/88 y to the 100. This is minus, or you could say negative, 1/44 y to the 100th. And so we can add these two terms together. This is going to be, we could write this, one over 88 minus one over 44 y to the 100th, and then you have plus one, plus 1/2, so that's pretty straightforward. So you have plus one, plus 1/2, so that's gonna be plus 3/2, plus 3/2. And now we just have to figure out what this is. So 1/88 minus 1/44, well, the common denominator here could be 88. That is the least common multiple of 44 and 88. 88 is divisible by 44. So if we multiply the denominator by two, you get 88. You multiply the numerator by two, you get two. 2/88 is the same thing as 1/44. So this 1/88 minus 2/88. Well, this is going to give us, this right over here is going to give us, if we, this is going to give us minus, or negative, 1/88. 1/88 minus 2/88 is going to be negative 1/88, y to the 100, y to the 100, plus 3/2, plus 3/2. And that is negative 1/88th y to the 100th, y to the 100th plus 3/2. This choice right over here.