Part a: the area of a square is (25x2 − 40x + 16) square units. determine the length of each side of the square by factoring the area expression completely. (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. (5 points) (10 points)

Step-by-step explanation:

25x2 − 40x + 16 = (5x)² - 2*5*4  + 4²      { (a - b)² = a² - 2ab + b² }

                           = (5x - 4)²                      { here a = 50 and b = 4}

Side of the square = 5x - 4 units

Part B:

25x2 − 16y2 = (5x)² - (4y)²         { a² - b² = (a + b) * (a - b) }

                     = (5x + 4y) * (5x - 4y)    { here a = 5x and b = 4y}

Dimensions of Rectangle: (5x + 4y) ; (5x - 4y)

see explanation

Step-by-step explanation:

A

25x² - 40x + 16 ← is a perfect square of the form

(ax - b)² = a²x² - 2abx + b²

Comparing the coefficients of like terms in the 2 expressions

a² = 25 ⇒ a = 5, b² = 16 ⇒ b = 4

and 2 × 5 × 4 = 40, thus

25x² - 40x + 16 = (5x - 4)²

The side of the square = 5x - 4

B

25x² - 16y² ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

25x² - 16y²

= (5x)² - (4y)² = (5x - 4y)(5x + 4y)

Dimensions of rectangle are 5x - 4 and 5x + 4