Part A: The area of a square is (9x2 − 12x + 4) 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 (25x2 − 16y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points) (10 points)

The length of each side of the square = (3x - 2) units

The dimensions of the rectangle = (5x + 4y) units & (5x - 4y) units

Step-by-step explanation:

Part A

Given:

Area of square = (9x^2 - 12x + 4) sq. units

To find:

The length of each side of the square = ?

Solution:

9x^2 - 12x + 4 = 0

(3x)^2 - 2(3x)(2) + (2)^2 = 0

(3x - 2)^2 = 0   {Applying a^2 - 2ab + b^2 = (a - b)^2}

3x - 2 = 0        3x - 2 = 0

Therefore,

The length of each side of the square = (3x - 2) units

Part B

Given:

Area of rectangle = (25x^2 - 16y^2) sq. units

To find:

The dimensions of the rectangle = ?

Solution:

25x^2 - 16y^2 = 0

(5x)^2 - (4y)^2 = 0

(5x + 4y)(5x - 4y) = 0  {Applying a^2 - b^2 = (a + b)(a - b)}

Therefore,

The dimensions of the rectangle = (5x + 4y) units & (5x - 4y) units

2

step-by-step explanation:

1+1=2

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d