About this video
This problem simplifies an algebraic expression with the variable y raised to the 100th power. The video distributes the subtraction, combines the like y to the 100th terms by finding a common denominator of 88 so that one over 88 minus one over 44 equals negative one over 88, and adds the constant terms 1 and 1/2 to get 3/2. The equivalent expression is negative one eighty-eighth y to the 100th plus three halves.
You'll be able to
- distribute a negative sign across a parenthesized expression.
- add fractions with different denominators by finding a common denominator.
- combine like terms with a large exponent to match an equivalent expression.
Key words
- Distributing a negative
- Multiplying every term inside parentheses by negative one when a minus sign comes before them.
- Like terms
- Terms with the same variable and exponent, which can be added or subtracted directly.
- Common denominator
- A shared multiple of the denominators of fractions, used to add or subtract them.
- Least common multiple
- The smallest number that is a multiple of two given numbers, such as 88 for 44 and 88.
- Equivalent expression
- An expression that has the same value as another for every input.
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.
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