Question 321127: Factor the following
4x^2+12xy+9y^2
2x^3-20x^2+32x
28y^3-13y-6
8p^3-q^9
x^6-y^6
Answer by ehollins1(8)   (Show Source):
You can put this solution on YOUR website! 1)4x^2+12xy+9y^2=
( x+ y)( x+ Y) possible factors for 4: 1,2,4
(2x+ y)(2x+ y) possible factors for 12: 1,2,3,4,6,12 and possible factors for 9: 1,3,9
(2x+3y)(2x+3y)
*****check solution*****
=(2x+3y)(2x+3y)
=(2x*2x)+(2x*3y)+(3y*2x)+(3y*3y)
=4x^2+6xy+6xy+9y^2
=4x^2+12xy+9y^2
2)2x^3-20x^2+32x=
( x- )( x - x) possible factors for 2: 1,2
(2x- )(1x - x) possible factors for 20: 1,2,4,5,10,20 and possible factors for 32: 1,2,4,8,16,32
(2x-4)(1x^2-8x)
*****check solution*****
=(2x-4)(1x^2-8x)
=(2x*1x^2)-(2x*8x)-(4*1x^2)+(4*8x)
=2x^3-16x^2-4x^2+32x
=2x^3-20x^2-32x
3)28y^3-13y-6= already simplified (prime)
possible solutions (2y+2)(14y^2-3)but due to the middle value being -13y no possible factors can be placed to obtain that value and complete the problem properly.
4)8p^3-q^9= already simplified (prime)
Possible solution: substitution p=??, q=?? - none provided, not able to simplify
5)x^6-y^6= already simplified (prime)
Possible solution: substitution x=??, y=?? - none provided, not able to simplify
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