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

And then you make some assumptions about it.

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.

So what does this simplify to?

And all of these are divisible by 5.

So let's multiply both sides by mu.

Times v1 dot v1.

So this whole expression simplifies to

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

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.

Colour, Floyd Steinberg, CMYK, simpler

Color, Floyd Steinberg, CMYK, simpler

We have one expression on top of another expression.

The numerator has the same degree as the denominator.

That means reducing taxes on business, not raising them.

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 you could leave it this way, or you could actually try to simplify this a little bit.

We have 7 times 10 to the fifth over 2 times 10 to the negative 2 times 2.5 times 10 to the ninth.

Times negative one.

What's that going to simplify to?

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

And this number is the same as this number.

We have all of that over minus 16.

Marketing people have never been able to do that.

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

And I'll show you how that's done in a reasonably fair way.

We've stated the domain.

This is where we just get our algebra hat on, and try to simplify until it's a separable equation in v.

No, my brougham is waiting.

Remember, this thing is just this thing right here, we're just doing the Pythagorean theorem.

We've seen how expensive it would be to track all the photons in a scene.

So 4 9 is the exact same thing as 16 36.

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.

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

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

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.

And the only times that g of x is equal to 0 is when x is equal to negative 2 or x is equal to negative 8.