DISTRIBUTIVE PROPERTIES 

Hey guys its Voldemort or some what, the "Fortune Teller". I will be showing you how to simplify

expressions with distributive properties with 3 examples from our booklets. And those examples are:

-6+5(8-k)-8k

(Question 9 page 24 What happened to Ray Floob after he fell off Empire State building) 

(4x-9)+8(2x+3)-7x

(Question 12 page 25 What should you NOT do if you want to help get rid of graffiti) 

11-(3x-6)+2(4x+5)-x

(Question 13 page 25 What should you NOT do if you want to help get rid of graffiti)

Lets get on to it. First expression is -6+5(8-k)-8k. So what you want to go first is the brackets because of the order of operations, BEDMAS. 

Brackets 

Exponents

Division 

Multiplication

Addition 

Subtraction

Cause of that we have to do the multiplication in the brackets. What you want to do is you take the coefficient on the left hand side of the brackets and multiply that with the terms in your brackets. It should look something like this.

-6+5(8-k)-8k

(+5 groups of 8)

(+5 groups of -k)

-6+40-5k-8k 

Now you want to put your terms in order from(coefficient)variables to the constant and the answer. 

So now it should look something like this:

-5k-8k-6+40

Next step is you want to combine the like terms in your expression. It should look like this: 

-12k+34 

You have simplified this expression! Good for you! Can you answer the next expression? Lets see if you could do it! Next expression is (4x-9)+8(2x+3)-7x. Since there is no constant before the first pair of brackets, you automatically multiply that by positive one. SOOOOO, that basically re writing it without the brackets. It should look something like this: 

(4x-9)+8(2x+3)-7x

(+1 groups of 4x)

(+1 groups -9)

(+8 groups of 2x)

(+8 groups of +3) 

4x-9+16x+24-7x

Now what you want to do is put all the terms in order.

4x+16x-7x-9+24

Now you want to combine all like terms in order to simplify this expression, after this step, you are finished. 

13x+15.

And that's what you are left with. So that is the simplified version of that expression. Lets do one more just to get everything cleared with. Next expression is 11-(3x-6)+2(4x+5)-x. Spot anything different?? Yup! The constant before the brackets doesn't have a digit! It's just the negative sign. But it's no problem. That would equal a -1 because there is only one negative sign. 

- is the same thing as -1 

+ is the same thing as +1 

In order to solve this is the same thing as if it had the digit so it'll look like this: 

11-(3x-6)+2(4x+5)-x

(-1 groups of 3x)

(-1 groups of -6) 

(+2 groups of 4x) 

(+2 groups of +5) 

11-3x+6+8x+10-x

Same thing as before, now you want to put your terms in order: 

-3x+8x-x+11+6+10 

And now you combine all your like terms to get your simplified expression: 

4x+27 

That's it! You've done it! That's how you simplify expressions with distributive properties.

#LETSGOMATH