2. (08.05, 08.06 MC)
Part A: The area of a square is (16x2 + 24x + 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 (4x2 − 49y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

23 points and brainliest!!

see explanation

Step-by-step explanation:

A

The area of the square is

16x² + 24x + 9 ← this is a perfect square of the form

(ax + b)² = a²x² + 2abx + b²

Compare coefficients of like terms

comparing coefficient of x² terms

a² = 16 ⇒ a = = 4

compare  constant terms

b² = 9 ⇒ b = = 3

and 2ab 2 × 4 × 3 = 24

Thus

16x² + 24x + 9 = (4x + 3)²

length of each side of the square is 4x + 3

B

Given the area of the rectangle is

4x² - 49y² ← this is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

Then

4x² - 49y²

= (2x)² - (7y)²

= (2x - 7y)(2x + 7y)

The dimensions of the rectangle are (2x - 7y) and (2x + 7y)

step-by-step explanation: