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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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)

Mathematics
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Can someone help me
hi
Part A. Factor 9x2 − 12x + 4 This trinomial follows the pattern \(a^2 - 2ab + b^2 = (a - b)^2\)
ok im gonna plug it in
one sec
To factor it, first, what is it whose square is to 9x^2?
um..
idk
What do you square to get 9x^2? ___ * ___ = 9x^2 What is the square root of 9?
What number times itself equals 9?
3
Good. What times itself is x^2?
1
wait no
nothing
No. 1 * 1 = 1 The answer is x. x * x = x^2 Ok?
okay
That means (3x)(3x) = 9x^2 The square root of 9x^2 is 3x
ok
Now we deal with the 4. What is the square root of 4?
2
Good. Since we have the pattern: \(a^2 - 2ab + b^2 = (a - b)^2\) in this case we have: \(9x^2 - 12x + 4 = (3x - 2)^2\)
That means the side of the square is 3x - 2 units
so thats the length of each side?
Yes. Since it's a square, all sides measure 3x - 2
ooh okay thankyou
can you help with B?
In part B, you have a rectangle. A rectangle may or may not be a square. We need to factor (25x2 − 16y2)
(5x+4y)(5x−4y)
Here, the pattern of the binomial is: \(a^2 - b^2 = (a + b)(a - b) \) This is called the difference of two squares.
You are correct. As you can see the sides are not equal, so this rectangle is not a square.
Two opposite sides have length 5x + 4y, and the other two opposite sides have length 5x - 4y

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