**Multiplying Polynomials by Monomials**

Greetings ladies and germs! Today in class we learned about multiplying polynomials by monomials. Let's start off with a little explanation.

Usually we add the numbers in the bracket together than multiply the bracket by the constant.

**4 (2 + 4) = 4 (6)**

**= 24**

Is there another way we can do this?

What about multiplying each part of the bracket by 4?

*4 (2 + 4) = 4(2) + 4(4)*

*= 8 + 16*

*= 24*

The answer is the same.

Here's another example.

*5 (6-3) = 5(3)*

*= 15*

Once again let's use our method.

*5 (6 -3) = 5(6) -3(5)*

*= 30 - 15*

*= 15*

The answer is the same.

How about something more complex?

*2x (3x + 4)*

We can still do the same thing as before.

*2x (3x + 4) = 2x(3x) +2x(4)*

*= 2(3)(x)(x) + 2(4)(x)*

*= 6 x^2 + 8x*

It's the same concept. It just takes a bit more time to do.

Can we represent this with a picture? We sure can!

*5 x (-2x +y -2)*

Let's do a multiplication diagram for this.

The solution is

*-10x^2 + 5xy - 10x*Now I'll show you how to do the reverse. Finding the equation when you have the diagram.

Remember that the first part of the polynomial is on the left side of the diagram.

In this case *-2x *is the first part. *3x -4 *is the other part.

So the formula is *-2x (3x - 4)*

Now we solve!

*-2x (3x -4) = -2x (3x) - 4 (-2x)*

*= -6x^2 + 8x*

Some common mistakes people make when multiplying polynomials by monomials is...

1. Forgetting to look at the signs. Instead of making a number negative, you make it positive and vice versa

2. You forget to multiply all the terms in a polynomial. This one is kind of self-explanatory. REMEMBER TO MULTIPLY ALL THE TERMS!

Okay people! Here's the homework.

- Read Pages 264 -268

- Check your Understanding 2 and 3

- Practise 0dd or even

- Apply All

- Extend 2 of 3

- And the 7.4 Green sheet we got ages ago.

- And last but certaionly not least... MANGAHIGH!!! We are in a Fai-To!!!

If you have questions please ask. If not, then I bid you *adieu.*

Oh yeah I almost forgot. The next blog person is......... ANA LOPENA