The leading coefficient here, the coefficient on the highest degree term in standard form it's already in standard form

It looks she's taking her compass, she's probably putting one of the points here, she put one of the points there and then she kind of drew this arc. And then it looks like she put the point there and then she drew that arc.

Zero Squared to zero squared to zero squared which is of course, just equal to zero.

And then let me get the x terms, so 4x and 7x. So this is plus 4x plus 7x.

Negative 2 plus 1 is negative 1x squared.

So this first part we can just write as 2a squared b, minus 3ab squared, plus 5a squared b squared.

So x squared over y squared is equal to x over y squared.

So we know that a squared plus b squared is equal to c squared.

So let's use that notion to do some multiplication. So if we say 2x minus 1, times 2x plus 1.

You can't do this for just any binomial multiplication.

So 3 squared is equal to r squared.

And I'm going to add that to 7x plus x squared.

Here I have an a squared b.

Well, these are the same thing.

But anyway, that the area of this larger square is also the area of these four triangles, plus the area of this smaller square. So this, the area of the larger square, which we figured out just by taking the... taking one side of it and squaring it, that should be equal to the area of the four smaller triangles, so there's four of them. And what's the area of each of them?

So times 10 e to the minus x squared plus y squared plus z squared.

So the radius away from the center, that's just going to be r squared is just x squared plus y squared plus z squared.

So minus x squared plus y squared plus z squared, with respect to x.

This is the hypotenuse. So x squared plus 5 squared plus 25 is going to be equal to the hypotenuse squared, it's equal to 100. x squared is equal to 100 minus 25, 75. x is equal to the square root of 75.

Well this is x squared over y squared.

X2 minus x1 minus 5 squared over sigma squared.

But let's just go through this step by step.

You saw that earlier in the video, when we were multiplying, when we were taking squares.

And then 2 plus 1 squared.

And 4a squared times minus 5 is minus 20a squared.

The coefficient here is 11.

Let's do another one of these examples.

Do I have any other ones? Well, yeah sure, the next term is.

But I just want to show you that I'm just adding negative 2 to 1 there. Then I have 4x plus 7x is 11x.

So we did indeed get the same answer. Let's do one more, and we'll do it the fast way. So if we have 8x minus 3 actually, let me do one which has more variables in it.

So we know that a squared plus 3 squared is equal to the hypotenuse squared, the side opposite the 90 degree angle.

And that's just minus 2z times 10 e to the minus x squared plus y squared plus z squared.

The square of 5 is 25.

It's like an x squared curve like that.

So that's 16t squared.

Plus 16t squared.

It's x squared over 2.

Well that's 1 squared.

It's b squared.

All of that over 2 times c all of that over 32.

2 squared is 4.

Second squared's cancel out.

23 squared, OK.

93 squared.

Well, same idea.