Question

WILL MARK BRAINLIEST!!!!

Answer 1

Answer:

Step-by-step explanation:

1. the area of square is 9x^2-12x+4 square units

shortcut: (a-b)^2= a^2-2ab+b^2

then simplify 9x^2-12x+4 to (3x-2)^2

area of square = s^2

then side equals sqrt((3x-2)^2)

s = (3x-2) units

2. the area of rectangle is (25x^2-16y^2) square units

shortcut: (a^2-b^2) = (a-b)(a+b)

then simplify (25x^2-16y^2) to (5x-4y)(5x+4y) square units

one side is: (5x-4y) units

one side is (5x+4y) units

Answer 2

Answer:

See below.

Step-by-step explanation:

SQUARE:

The area of the square is:

$9x^2-12x+4$

Factor it:

$=9x^2-6x-6x+4\\=3x(3x-2)-2(3x-2)\\=(3x-2)(3x-2)\\=(3x-2)^2$

Remember that all four sides of a square is equal. The area is simply the side squared. Therefore, all four sides of the square measure (3x-2).

RECTANGLE:

$25x^2-16y^2$

Factor it. This resembles the difference of two squares, where:

$(x-a)(x+a)=x^2-a^2$

$25x^2-16y^2\\=(5x)^2-(4y)^2\\=(5x-4y)(5x+4y)$

This cannot be simplified further. Note that the sides of rectangles doesn't necessarily have to be the same.

The dimensions of the rectangle is:

(5x-4y) by (5x+4y)