Another one where they're trying to get the simplest form.

So what does this simplify to?

And all of these are divisible by 5.

So let's multiply both sides by mu.

You see, remarked Holmes, as we paced to and fro in front of the house, this marriage rather simplifies matters.

The length is given right over there it is a squared plus 6 a minus 27 they want us to simplify this.

Colour, Floyd Steinberg, CMYK, simpler

Color, Floyd Steinberg, CMYK, simpler

And then you make some assumptions about it.

I'm starting to see the light at the end of the tunnel.

let's cancel that out.

25i 2 is the same thing as 25 times 1, so that is 25.

You would get 8 minus 4 is 4.

And that can also be written as and this is my preferred notation, because it doesn't have all this extra junk everywhere.

The trick here is to factor it and simplify it before you do any multiplication.

Times v1 dot v1.

And this number is the same as this number.

We have all of that over minus 16.

So this whole expression simplifies to

Is given right up here, is 2x times the principal square root of 5 minus 4, minus 4.

We maximized the posterior probability of data logarithmic is a monotonic function, and I put a minus sign over here so the optimization problem becomes a minimization problem.

We have one expression on top of another expression.

let's cancel that out.

Well, a is minus 10, so 2 times a is minus 20.

We have a b squared over b to the third power

You could bring the 13 down here if you want to write it so you don't have a fraction over a fraction.

It has a magnetic quality that draws me in.

Times negative one.

What's that going to simplify to?

Minus va minus 400 12.

Let's do another problem.

In future videos we'll do really hairy problems where you have to simplify it into this form so that we know that it definitely is an ellipse.

And then we distributed this x times x plus two, and this three times x plus two, and simplify.

We inject our own aerosols into the atmosphere, and we have trace gases, and not just carbon dioxide it's methane, ozone, oxides of sulfur and nitrogen.

Because if we just simplify this expression, and we include things in the simplified domain that weren't included in the original function's domain, we've actually changed the expression.

All we did is wherever we saw an x, we substituted it, minus 2 there.

But because this is an equation, it equals 0, let's just divide everything by 9.

We've stated the domain.

These will make this expression undefined. It will make this denominator equal to 0.

The numerator has the same degree as the denominator.

So we start with 5x 2(7x 1) 14x

And let's see what this simplifies to.

So we can do this in multiple ways, simplify different parts.

So let's factor out a 6. And then 12x divided by 6 is 2x. And then 30 divided by 6 is 5.

So we can write this as x plus 2 times x plus 8.