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) (10 points)

The length of each side of the square = (3x - 2) units

The dimensions of the rectangle = (5x + 4y) units & (5x - 4y) units

Step-by-step explanation:

Part A

Given:

Area of square = (9x^2 - 12x + 4) sq. units

To find:

The length of each side of the square = ?

Solution:

9x^2 - 12x + 4 = 0

(3x)^2 - 2(3x)(2) + (2)^2 = 0

(3x - 2)^2 = 0   {Applying a^2 - 2ab + b^2 = (a - b)^2}

3x - 2 = 0        3x - 2 = 0

Therefore,

The length of each side of the square = (3x - 2) units

Part B

Given:

Area of rectangle = (25x^2 - 16y^2) sq. units

To find:

The dimensions of the rectangle = ?

Solution:

25x^2 - 16y^2 = 0

(5x)^2 - (4y)^2 = 0

(5x + 4y)(5x - 4y) = 0  {Applying a^2 - b^2 = (a + b)(a - b)}

Therefore,

The dimensions of the rectangle = (5x + 4y) units & (5x - 4y) units

homozygous. one is homozygous, while two is heterozygous.

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step-by-step explanation: