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)

- anonymous

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- anonymous

@Keigh2015

- anonymous

@Kash_TheSmartGuy

- anonymous

@phi

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## More answers

- anonymous

Can someone help me

- anonymous

hi

- mathstudent55

Part A.
Factor 9x2 − 12x + 4
This trinomial follows the pattern
\(a^2 - 2ab + b^2 = (a - b)^2\)

- anonymous

ok im gonna plug it in

- anonymous

one sec

- mathstudent55

To factor it, first, what is it whose square is to 9x^2?

- anonymous

um..

- anonymous

idk

- mathstudent55

What do you square to get 9x^2?
___ * ___ = 9x^2
What is the square root of 9?

- mathstudent55

What number times itself equals 9?

- anonymous

3

- mathstudent55

Good.
What times itself is x^2?

- anonymous

1

- anonymous

wait no

- anonymous

nothing

- mathstudent55

No. 1 * 1 = 1
The answer is x. x * x = x^2
Ok?

- anonymous

okay

- mathstudent55

That means (3x)(3x) = 9x^2
The square root of 9x^2 is 3x

- anonymous

ok

- mathstudent55

Now we deal with the 4.
What is the square root of 4?

- anonymous

2

- mathstudent55

Good.
Since we have the pattern:
\(a^2 - 2ab + b^2 = (a - b)^2\)
in this case we have:
\(9x^2 - 12x + 4 = (3x - 2)^2\)

- mathstudent55

That means the side of the square is 3x - 2 units

- anonymous

so thats the length of each side?

- anonymous

@phi

- mathstudent55

Yes. Since it's a square, all sides measure 3x - 2

- anonymous

ooh okay thankyou

- anonymous

can you help with B?

- mathstudent55

In part B, you have a rectangle. A rectangle may or may not be a square.
We need to factor (25x2 − 16y2)

- anonymous

(5x+4y)(5x−4y)

- mathstudent55

Here, the pattern of the binomial is:
\(a^2 - b^2 = (a + b)(a - b) \)
This is called the difference of two squares.

- mathstudent55

You are correct. As you can see the sides are not equal, so this rectangle is not a square.

- mathstudent55

Two opposite sides have length 5x + 4y,
and the other two opposite sides have length 5x - 4y

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