And when you factor by grouping, you're going to split up this term, this 15x.

You want to group it, one of them with this 2x squared and one of it with the 20.

Precedence and Associativity,

And so you multiply all the numerators

If you take each of those numbers that you're squaring, take their product and multiply it by 2, you have that right there.

So just to remind you, here's some code for computing the clustering coefficient of a graph with respect to a particular node v.

I think you see what I did.

looks like a squared.

Now if we multiply both sides by x plus 2, x plus 2 is a negative number.

That's interesting.

That equals a squared minus b squared.

We have an x plus 3 there.

If I have 2 to the seventh to the third power, well, here I multiplied the exponents.

So in this example what's A?

Remember the notation, the sum of squares and mean squares.

Well, that's just positive 4.

The last question asked, what is the maximum clustering coefficient for a node in B?

This means it takes less time to do our recursive walk and interpret it, and we have fewer multiplications.

And you can only add imaginary terms to each other.

Now, we take that 4x squared and we multiply it by our expression.

That equals x to the seventh.

And then 10 to the negative 2 times 10 to the ninth, when you multiply two numbers that are being raised to exponents and have the exact same base so it's 10 to the negative 2 times 10 to the negative 9 we can add the exponents.

Now let's think about what happens when we scale our vectors.

Multiply

Multiplication

And X1 and X2. Okay?

And then multiply that by 3, it's 12, just multiplying fractions.

And don't take my word for it.

Afterwards, we have about a dozen or so binary rules.

And now see if you can factor the denominator. And this one's more straightforward. The coefficient here is 1.

So, I just said and look, the a is just the coefficient on the x term, right? a is the coefficient on the x squared term. b is the coefficient on the x term, and c is the constant.

Well, A is the coefficient on the x squared term.

So that's our third exponent rule, that when I raise an exponent to a power, and then I raise that whole expression to another power,

As long as I multiply the numerator and the denominator by the same number I'm just multiplying my 1, so I'm not changing anything.

In this video, I want to tackle some inequalities that involve multiplying and dividing by positive and negative numbers, and you'll see that it's a little bit more tricky than just the adding and subtracting numbers that we saw in the last video.

One definition of exponentiation is that you start with a one, you start with a one, then you multiply this number times a one once.

We just have to multiply both sides times the reciprocal of the coefficient on the left hand side.

Two times the number of links divided by length of neighbors times length of neighbors minus one.

And then in the second segment we'll take a more mathematical approach.

If you go back and look at the scatter plot, you sort of see how we would get that value.

If you look at that data between axes x and y,

Well, remember, in all of these problems where you have a non 1 or non negative 1 coefficient here, we look for two numbers that add up to this, whose product is equal to the product of that times that.

So when you multiply by 3, you're adding the number to itself three times.

I could just draw it like this.

So first of all, I have a positive 3 here.