Question

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

Answer 1

Part B: The dimensions are (4x + 3y) and (4x - 3y)

Explanation:

our equation is: (16x^2 - 9y^2)

With this equation, we must plug it into the formula: (a + b)(a - b) = a^2 - b^2

so,

a^2 = 16x^2

b^2 = 9y^2

then,

a = sqrt(16x^2) = 4x

b = sqrt(9y^2) = 3y

(these are the correct variables because 3*3 = 9, and 4*4 = 16)

now, we plug this information back into the formula again;

(a + b)(a - b) = (4x + 3y)(4x - 3y)

therefore, (4x + 3y)(4x - 3y) is the answer!

I hope this helps, have a wonderful day!

Answer 2

Explanation:

4x² - 12x + 9 = ?

4x² - 12x + 9 = 4x²- 6x - 6x + 9 = 2x

2x(2x - 3) - 3(2x - 3)

(2x - 3)(2x - 3)

(2x - 3)²

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