Part A: The area of a square is (4x2 − 12x + 9) 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 (16x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Step-by-step explanation:

A )   a²- 2ab + b² = (a - b)²

4x² - 12x + 9 =  (2x)² - 2 *2x *3 + 3²

                    = (2x - 3)²

Length of each side of a square = 2x -3

b) a² - b² = (a +b)(a - b)

16x² - 9y² = 4²*x² - 3²*y²

                = (4x)² - (3y)²

                = (4x + 3y) (4x - 3y)

Dimensions of rectangle are :  (4x +3y); (4x - 3y)

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d

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