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.

Answer 1

We know that the area of a rectangle is given by the product of its length and width. Let the length of the rectangle be represented by 16x2 and its width by -9y2. This may initially seem counterintuitive due to the negative sign, but it is necessary for factoring later on.

Therefore, we have:

Area = length x width
(16x2) (-9y2) = -144x2 y2

To factor this expression, we can use the difference of squares formula:

a2 - b2 = (a + b)(a - b)

In our case, a = 4x and b = 3y, so:

144x2 y2 = (4x)2 - (3y)2
= (4x + 3y)(4x - 3y)

Therefore, the dimensions of the rectangle are:

Length = 4x + 3y
Width = 4x - 3y

Answer 2

Can you paraphrase your answer

Answer 3

To determine the dimensions of a rectangle given its area expression of (16x2 − 9y2) square units, we need to factor it completely. The product of length and width will give us the area of the rectangle. Assuming the length to be 16x2 and the width to be -9y2, we can express the area as (-144x2 y2). To factor this expression, we can use the difference of squares formula, which gives us the factors (4x + 3y) and (4x - 3y). Hence, the dimensions of the rectangle are Length = 4x + 3y and Width = 4x - 3y.