anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@Haseeb96
anonymous
  • anonymous
@undeadknight26
anonymous
  • anonymous
@welshfella

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welshfella
  • 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
  • anonymous
Idk, 4 square root is 2 right?
welshfella
  • welshfella
yes what about 9x^2?
welshfella
  • welshfella
u need square root of 9 and square root of x^2
anonymous
  • anonymous
3, idk how to get the square root of x^2
welshfella
  • welshfella
its easy x^2 = x * x so by definition square root of x^2 = x so square root of 9x^2 = 3x
welshfella
  • 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
  • anonymous
Makes sense
welshfella
  • welshfella
thats 9x^2 on last line not x^2
anonymous
  • anonymous
So what would that get for part A?
welshfella
  • welshfella
Part B is a rectangle with different length and width
welshfella
  • welshfella
- we finished part A
anonymous
  • anonymous
Wait, what was the answer for part a? x^2 - 12 x + 4 = (3x - 2)^2 ?
welshfella
  • welshfella
yea those are the factors and side length = 3x - 2
anonymous
  • anonymous
Sweet, now what would part b be? how would we find it?
welshfella
  • 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
  • anonymous
5x^2, 4x^2?
welshfella
  • 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
  • welshfella
nearly right NOT 4x^2
anonymous
  • anonymous
2x^2?
welshfella
  • welshfella
you have the number paret right - 5 and 4 but what are sqrts of x^2 and y^2?
anonymous
  • anonymous
x*x
welshfella
  • welshfella
no x^2 = x*x - i wan the square root of x^2
welshfella
  • welshfella
check back to earlier posts
anonymous
  • anonymous
x?
welshfella
  • welshfella
yes the square root of x^2 = x because x*x = x^2 similarly sqrt y^2 = y
welshfella
  • welshfella
so sqrt 25x^2 = 5x and sqrt 16y^2 = ?
anonymous
  • anonymous
2x?
welshfella
  • welshfella
why 2x - there's no x in 16y^2 and sqrt 16 is not 2 - its 4
anonymous
  • anonymous
so it's just 4
welshfella
  • welshfella
4 is aqrt 16 yes but i need sqrt of 16y^2
anonymous
  • anonymous
4x?
welshfella
  • 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
  • anonymous
Square root of ^2 is x? waaait im wrong
anonymous
  • anonymous
there is none, so why wouldn't it just be 4??
anonymous
  • anonymous
4y!!!!!!!!??
welshfella
  • welshfella
yes - of course 4y
welshfella
  • welshfella
so going back 25x^2 - 16y^2 = ( 5x + 4y)(5x - 4y) note there's + in one bracket and - in the other
welshfella
  • welshfella
those are the factors and the dimensions of the rectangle one dimension is 5x+4y and the other ix 5x-4y.
anonymous
  • anonymous
So that's the answer, 5x+4y for each side?
welshfella
  • welshfella
no 5x+4y for one side and 5x-4y for the other
welshfella
  • welshfella
5x+4y will be the length and 5x-4y will be the width
anonymous
  • anonymous
Thanks!!
welshfella
  • welshfella
yw

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