1. Before 10.7 Review of the Distributive Property

3. You can find the area of the two separate rectangles and add the two areas together or you can find the area of one large rectangle. AB Rectangle A had dimensions of 30 by x. The area of A is 30x. Rectangle B had dimensions of 30 by 10. The area of B is 300. The combined area is 30x + 300. If I look at the pool as one big rectangle the side lengths will be 30 by (x+10). I can use the distributive property to multiply 30(x+10) The combined area is 30x + 300.

4. Rectangle A had dimensions of 25 by x. The area of A is 25x. Rectangle B had dimensions of x by x. The area of B is x 2. The combined area is 25x + x 2. If I look at the pool as one big rectangle the side lengths will be x by (x+25). I can use the distributive property to multiply x(x+25) The combined area is x 2 + 25x. You can find the area of the two separate rectangles and add the two areas together or you can find the area of one large rectangle. B A

5. This one can be done in more than two ways. I can split it up into 4 smaller rectangles. Or I can make two tall rectangles. Or I can make two wide rectangles. Or I can write it as finding the area of one large rectangle. A As one large rectangle the side lengths would be (x+2) and (x+3) The combined area is x 2 + 5x +6. To get that area, I would have done one of the other methods to still get the area of the parts. Rectangle A had dimensions of x by x+2. The area of A is x(x+2) = x 2 +2x Rectangle B had dimensions of 3 by x+2 The area of B is 3(x+2) = 3x+6 The combined area is x 2 + 5x +6 A B

6. Rectangle X had dimensions of a by b. The area of X is ab. Rectangle Y had dimensions of a by c. The area of Y is ac. The combined area is ab+ac. If I look at the pool as one big rectangle the side lengths will be a by (b+c). I can use the distributive property to multiply a(b+c) The combined area is ab+ac. X Y You can find the area of the two separate rectangles and add the two areas together or you can find the area of one large rectangle.

8. aka Area as SUM = 3x + 15 = 2x 2 + 10 = 6x - 20 x 5 3 = x 2 +7x +10 3x -10 2 x 5 2x x x 2 5

9. aka Area as PRODUCT = 12(2x + 1) = x(x + 3) = 3x+6 = 3(x + 2) = (x+1)(x + 3) x x 1 3 x 3 x 2x 1 12