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)

Part A: (2x - 3) units

Part B: (4x + 3y) by (4x - 3y)

Step-by-step explanation:

Part A:

A = 4x² - 12x + 9

(a) Multiply the first and last terms

4 × 9= 36

(b) List all the factors of 36

1 × 36; 2 × 18; 3 × 12; 4 × 9; 6 × 6

(c) Find a pair of factors whose product is 36 and whose sum is -12.

After some trial and error, you will choose -6 and -6

-6 × (-6) = 36 and -6 + (-6) = -12.

(d) Rewrite -12x as -6x - 6x

A =4x² - 6x - 6x + 9

(e) Factor by grouping

A =2x(2x - 3) - 3(2x - 3)  

A = (2x - 3)(2x - 3)

Each side of the square is 2x - 3 units long.

Part B

A = 16x² - 9y² = (4x)² - (3y)²

A = (4x + 3y)(4x - 3y)

The dimensions of the rectangle are 4x + 3y long by 4x -3y wide.

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step-by-step explanation: