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