Multiply

Multiplication

And we learned, up here, in this part of the video,

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

So dividing by 1 2 is the exact same thing as multiplying by 2 1.

Well, the smallest number that is divisible by 4 and 8 is 8.

Precedence and Associativity,

We can divide both sides of this inequality by 3.

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

Never have to worry about that.

That's called dimension analysis.

Well, we have a little bit of experience doing this.

That minus two is here and this fourx is here.

Multiply, expressing the product in scientific notation.

We just substituted that for that to get this right here.

If volume goes down, pressure goes up, and that makes sense.

They have to be positive.

Now, we can just multiply both sides of this equation by minus thirteen over three.

And then our denonminator, two numbers.

This is just a review of grouping.

We have an x plus 3 there.

These are just multiple ways of stating the same thing.

Let me switch colors.

But just understand that this is the same thing as this.

OK.

So we got a lot of twos

So this is just our integration by parts formula.

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.

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

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

So we're going to have our precedence and associativity.

So if this is true, then the following must be true. c1 times 1 plus 0 times c2 must be equal to x1.

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

Let me do it in the right color. one times zero.

And you can only add imaginary terms to each other.

So we could write 3.457 3.457

Now sometimes when you see a proportion like this, sometimes you'll say oh you could cross multiply.

And notice we're getting the exact same value that we got with cross multiplying.

So let's do that.

And the reason is the math inside this sum is linear.

Let's do that.

Now there's one other really interesting thing about multiplication.

So you get equals x squared over a squared plus 1.

So if we assume that x is less than minus 4, then when we multiply both sides of this equation times x plus 4 and you're multiplying it by x minus 3 over x plus 4.

1 is definitely less than 2.