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)

Correct answer. Part A: (4 x + 3)²,  Part B: (2 x - 7 y) · (2 x + 7 y)

Step-by-step explanation:

Given:

This square trinomial is the complete square of the binomial whose formula

(a + b)² = a² + 2 · a · b + b²

16 x² + 24 x + 9 = (4 x)² + 2 ·(4 x) · 3 + 3² = (4 x + 3)² = (4 x + 3) · (4 x + 3)

The formula for the difference of squares  is.

a² - b² = (a - b) · (a + b)

4 x² - 49 y² = (2 x)² - (7 y)² = (2 x - 7 y )· (2 x + 7 y)

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