Question

Please simplify the two expressions and tell me how to do number 9 please

Answer 1

1) 12c-8            2) 6b             3) 126 square cm

Answer 2

For the first expression. move the like terms next to each other in the expression.

17c - 5c -3 + 5     Do -3 + 5
17c - 5c + 2          Pretend the c isn't there and do 17 - 5
12c + 2

For the second expression, pretend the b isn't there and do -12 + 10

8b -2b     Now, do 8 - 2
6b

For number 9, you know that since the top of the rectangle is 20cm, the bottom should be too. You can then use the 6cm and 2cm to find out how much of the bottom is missing.

20 - (6 + 2)   Add 6 and 2
20 - 8           Subtract
12

So, the base of the triangle is 12cm. The side of the rectangle tells you that the height of the triangle is 9cm. If you plug those numbers into the triangle area formula, you can find the area of the triangle.

1/2 (b x h)   Plug in the numbers ( b = 12 , h = 9)
1/2 (12 x 9)  Multiply 12 and 9
1/2 (108)      Find half of 180
54

The are of the triangle is 54$cm^{2}$. Since you need the area of the rectangle minus the are of the triangle, you need the are of the rectangle. That can be found using l x w.

l x w Plug in the values (l = 9 , w = 20)
9 x 20   Multiply
180 

Now, subtract the area of the triangle (54) from the area of the rectangle (180).

180 - 54   Subtract
126

The area of the shaded region is 126$cm^{2}$.