Question

MEDAL AND FAN :D


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

@Haseeb96

Answer 2

@undeadknight26

Answer 3

@welshfella

Answer 4

9x^2 - 12 x + 4
is a perfect square

can you tell me what are the square roots of 9x^2 and 4?

Answer 5

Idk, 4 square root is 2 right?

Answer 6

yes what about 9x^2?

Answer 7

u need square root of 9 and square root of x^2

Answer 8

3, idk how to get the square root of x^2

Answer 9

its easy x^2 = x * x
so by definition square root of x^2 = x

so square root of 9x^2 = 3x

Answer 10

we need -2 for square root of 4 because we have -12x in the middle of the expression
square root of 9x^2 - 12 x + 4
= (3x - 2)


x^2 - 12 x + 4 = (3x - 2)^2 = area of the square
each side of square has length 3x - 2

Answer 11

Makes sense

Answer 12

thats 9x^2 on last line not x^2

Answer 13

So what would that get for part A?

Answer 14

Part B is a rectangle with different length and width

Answer 15

- we finished part A

Answer 16

Wait, what was the answer for part a? x^2 - 12 x + 4 = (3x - 2)^2 ?

Answer 17

yea those are the factors and side length = 3x - 2

Answer 18

Sweet, now what would part b be? how would we find it?

Answer 19

25x^2 - 16y^2 is the Difference of 2 squares
this factors to 2 binomials which are the same except one has + and one has - sign

first what are the sqqaure roots of 25x^2 and 16y^2?

Answer 20

5x^2, 4x^2?

Answer 21

first square root of 25 = 5 and sqrt of x^2 = x giving 5x

so can you figure out square root of 16y^2 in a similar way?

Answer 22

nearly right NOT 4x^2

Answer 23

2x^2?

Answer 24

you have the number paret right - 5 and 4 but what are sqrts of x^2 and y^2?

Answer 25

x*x

Answer 26

no x^2 = x*x - i wan the square root of x^2

Answer 27

check back to earlier posts

Answer 28

x?

Answer 29

yes the square root of x^2 = x because x*x = x^2
similarly sqrt y^2 = y

Answer 30

so sqrt 25x^2 = 5x and sqrt 16y^2 = ?

Answer 31

2x?

Answer 32

why 2x - there's no x in 16y^2 and sqrt 16 is not 2 - its 4

Answer 33

so it's just 4

Answer 34

4 is aqrt 16 yes but i need sqrt of 16y^2

Answer 35

4x?

Answer 36

- u r driving me crazy!! - how can it be x when theres no x in 16y^2 - what letter is in 16y^2?

Answer 37

Square root of ^2 is x? waaait im wrong

Answer 38

there is none, so why wouldn't it just be 4??

Answer 39

4y!!!!!!!!??

Answer 40

yes - of course 4y

Answer 41

so going back
25x^2 - 16y^2 = ( 5x + 4y)(5x - 4y)

note there's + in one bracket and - in the other

Answer 42

those are the factors and the dimensions of the rectangle
one dimension is 5x+4y and the other ix 5x-4y.

Answer 43

So that's the answer, 5x+4y for each side?

Answer 44

no 5x+4y for one side and 5x-4y for the other

Answer 45

5x+4y will be the length and 5x-4y will be the width

Answer 46

Thanks!!

Answer 47

yw