About this video
Sal evaluates -2 circle-plus (3 circle-x -1), where x circle-x y = x + 3y and x circle-plus y = 4x^2 - y^2. He works out the parentheses first to get 0, then substitutes into the second definition to get 16.
You'll be able to
- evaluate a newly defined operator by substituting into its definition.
- evaluate nested operators by working from the inside out.
- square negative numbers correctly when substituting.
Key words
- Operator
- A symbol that tells you what to do with numbers; here circle-x and circle-plus are new ones.
- Substitute
- Put a given number in place of a variable in a rule.
Transcript
If x-- and the operator here is this x with a circle around it, so maybe we'll call it circle-x. If x circle-x y is equal to x plus 3y, and x-- I'll call that circle-plus. So it's not plus, it's a different operator. It's a new operation, and we're defining it here.
And x circle-plus y is equal to 4x squared minus y squared, find negative 2 circle-plus the quantity three circle-cross, or circle-x minus 1. So if we just break it down, we use these definitions, it should hopefully be pretty straightforward. So let's evaluate 3 circle-x negative 1.
So 3 circle-x negative 1. Well, they define that as whatever is x plus 3 times whatever is y. So this is going to be whatever is x, so that is our 3, plus 3 times whatever is y. Well, that's going to be negative 1. So this is 3 plus negative 3, which is equal to 0.
So this whole part right over here is equal to 0. So our entire expression simplifies down to negative 2 circle-plus 0. And now we can use this definition right here. x circle-plus y is equal to 4x squared minus y squared. So in this situation, our x-- let me circle it over here.
Our x is negative 2 , and our y is 0. So this is going to be equal to-- it's going to be equal to 4 times x squared. So that's negative 2 squared. 4 times negative 2 squared minus y squared. Well, y is just 0. Minus 0 squared. And 0 squared is obviously just 0.
And so this simplifies to 4 times negative 2 squared. Negative 2 squared is positive 4. So it's 4 times 4. So it simplifies to 4 times 4, which is equal to 16. And we're done.
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