URGENT WILL MARK BRAINLIEST + 15pts
Part A: The area of a square is (9x2 − 12x + 4) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (25x2 − 16y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

A) 3x-2

B) (5x-4y)(5x+4y)

Step-by-step explanation:

A) Area of a square = s²

9x²-12x+4

(3x)²-2(3x)(2)+(2)²

(3x-2)²

Each side is (3x-2)

B) Area of rectangle = length × width

25x²-16y²

(5x)²-(4y)²

(5x-4y)(5x+4y)

Step-by-step explanation:

Part A. The length of each side of the square is equal. The formula for determining the area of a square is Area = L²

Therefore,

L = √Area

The area of a square is (9x2 − 12x + 4) square units. To determine the length of each side, we would factorize the equation

9x² − 12x + 4

We would find two numbers such that their sum or difference is -12x and their product is 4x^2. The two numbers are - 6x and - 6x. Therefore,

9x² - 6x - 6x + 4

3x(3x - 2) - 2( 3x - 2)

(3x - 2)(3x - 2)

The length of each side is 3x - 2 units

Part B

The area of the rectangle is (25x² − 16y²) square units. Factorizing, it becomes

(5x - 4y)(5x + 4y)