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)

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Step-by-step explanation:

The area of a square is

A = s^2

(9x2 − 12x + 4) = s^2

Rewriting the left side by recognizing a perfect square trinomial

a^2 -2ab - b^2 = ( a-b) ^2

( 3x -2) ^2 = s^2

Taking the square root of each side

3x-2 = s

The side length is 3x-2

The area of a rectangle is

A =  l*2

25x^2 − 16y^2 = l*w

(5x)^2 - (4y)^2 = l*w

Rewriting the left side by recognizing a difference of squares

a^2  - b^2 = ( a-b) (a+b)

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

The dimensions are ( 5x-4y) by (5x+4y)

Step-by-step explanation:

The area of the triangle is 9x²-12x+4

To determine the length of this sqaure we must factor it in a way that we have two indentical expressions multiplide by each other

The length of the square is 3x-2

Th area is 25x²-16y²

The dimensions of this triangle are:

a

step-by-step explanation:

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