40 POINTS!
Please look at the two small pictures below. Here are the questions.
7. a) Write a multiplication statement to represent the algebra tiles. (picture #1)

b) If the tiles below are divided by 2x, what is the quotient?

Part a)

Part b)

Step-by-step explanation:

Part a)

I first determined what each piece in the rectangular array meant.

Then I wanted to figure out the height and the base length.

I know so that is why I put those purple 's on top and purple 's down alongside for the pieces. To get when I already had , I needed to multiply by -1 which is why there is a -1 along the top where those pieces are.

So in the first question down the side of the box, we have .

To find the area of the rectangle, you multiply height by base.

.

Part b)We have six 's and twelve 's. So that means the polynomial represented here is .

What happens if we divide that by .

Let's see:

A) 2x(2x - 5)

B) -(3x + 6)

Step-by-step explanation:

Each empty square represents: x²

Each filled rectangle represents: -x

Area is 4x² - 10x

There are two rows:

Each row is: 2x² - 5x = x(2x - 5)

Statement:

2x(2x - 5)

In b, there are 6 tiles of -x², and 12 tiles of -x, which makes it:

-6x² - 12x

-(6x² + 12x)

-(6x² + 12x)/2x

-[(6x²/2x) + (12x/2x)0

-(3x + 6)

-3x - 6