Question

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)

Answer 1

@Keigh2015

Answer 2

@Kash_TheSmartGuy

Answer 3

@phi

Answer 4

Can someone help me

Answer 5

hi

Answer 6

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

Answer 7

ok im gonna plug it in

Answer 8

one sec

Answer 9

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

Answer 10

um..

Answer 11

idk

Answer 12

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

Answer 13

What number times itself equals 9?

Answer 14

3

Answer 15

Good.
What times itself is x^2?

Answer 16

1

Answer 17

wait no

Answer 18

nothing

Answer 19

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

Answer 20

okay

Answer 21

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

Answer 22

ok

Answer 23

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

Answer 24

2

Answer 25

Good.
Since we have the pattern:

\(a^2 - 2ab + b^2 = (a - b)^2\)

in this case we have:

\(9x^2 - 12x + 4 = (3x - 2)^2\)

Answer 26

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

Answer 27

so thats the length of each side?

Answer 28

@phi

Answer 29

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

Answer 30

ooh okay thankyou

Answer 31

can you help with B?

Answer 32

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

Answer 33

(5x+4y)(5x−4y)

Answer 34

Here, the pattern of the binomial is:

\(a^2 - b^2 = (a + b)(a - b) \)

This is called the difference of two squares.

Answer 35

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

Answer 36

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