simplify m square - 4 over and square minus 3 and + 2 divided by M over M -1
Answers
Step-by-step explanation:
We're going to evaluate algebraic expressions at given values. What this means is we'll be given an expression and the first thing we'll do is we'll substitute in values for the variables. Then to finish the simplification, we'll simply go through the order of operations to determine which operation to apply next. The order of operation is just to remind all of us is to perform the computation inside the parentheses first, evaluate the exponents second, then multiply and divide in the order from left to right, followed by adding and subtracting in the order from left to right. Now here's a warm-up problem, we're going to evaluate this expression, which is x plus 3y cubed plus 8x divided by the quantity x plus y squared. And the given values we're evaluating at, well x will 4 and y will be negative 2. So, the first thing we do is we substitute in for x, which is here and here a 4 and then we'll substitute in the y value which is negative 2, we'll substitute it in here and here and that is that negative 2 you are seeing substituted in. Now, we have to simplify. And to simplify I'm going to go through order of operations. So, the very first thing I'm going to say is do I have parentheses? Can I work inside the parentheses first? Well, I definitely have parentheses, I have two sets of them. So, to work inside the parentheses, I have 4 plus 3 times negative 2, well that's 4 minus 6 which is negative 2. So, I simplified within the parentheses. Let's look at the second set of parentheses, I have 4 plus negative 2. Well, that's positive 2. Ok, so I simplified the parentheses, now I'm going to go through my checklist, how about the order of operations, what's next? Exponents. I have an exponent here and here. So, I'll cube my negative 2 that gives me negative, 8. I'll cube the 2, that gives me a 4. What's next on my order of operations? Well, we look for multiplying and dividing in the order from left to right and we have both in this term. Because I have negative 8, plus 8 times 4 divided by 4. So, in the order from left to right means 8 times 4 is 32 and then 32 divided 4 is 8, that's what we're referring to. The very last calculation is negative 8 plus 8 which is zero. Well now it's your turn, let's evaluate this algebraic expression when x is equal to 2 and when y is equal to negative 3. So, our first task we want to substitute in the value of 2 for x, so we'll place a 2 here and here, and we want to substitute in negative 3 for y, we'll place a negative 3 here. So, what does this next calculation look like? Well, we have 5 times 2 cubed, plus 3 times 2 times 2, plus 4 times negative 3 and that whole quantity looks like it's being what? It's being?