Question

Part A: The area of a square is (4x^2 - 12x + 9) square units. Determine the length of each side of the square by factoring the area expression completely.
Show your work.
Part B: The area of a rectangle is (16x^2 - 9y^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show
your work.

Answer 1

Answer: Area = side²

If Area = 4x² + 12x + 9, then the side is the √(4x² + 12x + 9)

Let’s factor 4x² + 12x + 9

What two numbers multiply to be 36 (which came from 4 * 9) add up to be 12?

6 and 6 are the two numbers, because 6 * 6 = 36, and 6 + 6 = 12.

We can break 4x² + 12x + 9 into (4x² + 6x) + (6x + 9)

Factor 4x² + 6x, the greatest common factor is 2x, so the 2x goes on the outside, leaving us with 2x + 3 on the inside, so that gives us 2x * (2x + 3).

Factor 6x + 9, the greatest common factor is 3, so the 3 goes on the outside, leaving us with 2x + 3 on the inside, that gives us 3 * (2x + 3).

Now we have the 4x² + 12x + 9 written as 2x (2x + 3) + 3 (2x + 3). Since we now have a common factor, 2x + 3, we can combine them by adding 2x (2x + 3) + 3 (2x + 3) as like terms, so we now have (2x + 3) * (2x + 3).

We can simplify (2x + 3)(2x + 3) into (2x + 3)².

There. The simplest factored form of 4x² + 12x + 9 is (2x + 3)²

Ok, the Area = (2x + 3)²

Let’s solve for the side

(2x + 3)² = side²

square root both sides and take the positive root

side = √(2x + 3)²

side = 2x + 3

The side length is: 2x + 3 units

I hope you get a good grade lol :)

Step-by-step explanation: