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# New operator definitions 2

Video 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.