Part: A The area of a square is (4a^2 - 20a + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.

Part B: The area of a rectangle is (9a^2 - 16b^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.

The length of each side of the square is (2a-5) units

Step-by-step explanation:

4a^2 - 20a + 25

= (2a) ^2 - 20a + (-5) ^2

= (2a - 5) ^2

Since the length of a square given a l produces an area l^2 then the length of the side l is the square root of the area l^2

length of side is therefore square root of (2a - 5) ^2 which is (2a-5)

The area of a rectangle whose one side is x and the other is y is xy, the product of x and y.

(9a^2 - 16b^2)

= (3a) ^2 - (4b) ^2 this is the difference of two squares, the factors are therefore

= (3a + 4b) * (3a - 4b)

The dimensions of the rectangle are:

one pair of opposite sides are 3a + 4b

and the other pair of opposite side perpendicular to the first pair is 3a - 4b