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)

- anonymous

- schrodinger

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- anonymous

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- anonymous

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## More answers

- welshfella

9x^2 - 12 x + 4
is a perfect square
can you tell me what are the square roots of 9x^2 and 4?

- anonymous

Idk, 4 square root is 2 right?

- welshfella

yes what about 9x^2?

- welshfella

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

- anonymous

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

- welshfella

its easy x^2 = x * x
so by definition square root of x^2 = x
so square root of 9x^2 = 3x

- welshfella

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

- anonymous

Makes sense

- welshfella

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

- anonymous

So what would that get for part A?

- welshfella

Part B is a rectangle with different length and width

- welshfella

- we finished part A

- anonymous

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

- welshfella

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

- anonymous

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

- welshfella

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?

- anonymous

5x^2, 4x^2?

- welshfella

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?

- welshfella

nearly right NOT 4x^2

- anonymous

2x^2?

- welshfella

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

- anonymous

x*x

- welshfella

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

- welshfella

check back to earlier posts

- anonymous

x?

- welshfella

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

- welshfella

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

- anonymous

2x?

- welshfella

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

- anonymous

so it's just 4

- welshfella

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

- anonymous

4x?

- welshfella

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

- anonymous

Square root of ^2 is x? waaait im wrong

- anonymous

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

- anonymous

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

- welshfella

yes - of course 4y

- welshfella

so going back
25x^2 - 16y^2 = ( 5x + 4y)(5x - 4y)
note there's + in one bracket and - in the other

- welshfella

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

- anonymous

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

- welshfella

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

- welshfella

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

- anonymous

Thanks!!

- welshfella

yw

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