SOLUTION: Factor: a) x^2-y^2+3x+y+2 b) 2x^2-3y^2-5xy+x+11y-6 c) x^2(y-z)+y^2(z-x)+z^2(x-y) I could only begin c) with expanding out the whole expression to: x^2(y)

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Question 541131: Factor:
a) x^2-y^2+3x+y+2
b) 2x^2-3y^2-5xy+x+11y-6
c) x^2(y-z)+y^2(z-x)+z^2(x-y)
I could only begin c) with expanding out the whole expression to:
x^2(y) - x^2(z) + y^2(z) - xy^2 - yz^2
I could not even attempt a) or b) and as mentioned above, I began c) with the expansion shown above.
Any assistance on these three problems would be greatly appreciated.
Answer by mananth(16949) (Show Source):
You can put this solution on YOUR website!
a) x^2-y^2+3x+y+2
Rewrite the equation
x^2+3x-y^2+y +2
complete the squares by splitting 2
9/4 -1/4 = 8/4 =2
(x^2+3x+9/4) -(y^2-y +1/4)
(x+3/2)^2- (y-1/2)^2
Difference of two squares
(x+3/2+y-1/2)(x+3/2-y+1/2)
(x+y+1)(x-y+2)
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b. It is a diophantine equation. to solve it there is a procedure. please look on net

c) x^2(y-z)+y^2(z-x)+z^2(x-y)
Using the direct formula for cyclic expressions
=-(x-y)(y-z)(z-x)
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SOLUTION: Factor: a) x^2-y^2+3x+y+2 b) 2x^2-3y^2-5xy+x+11y-6 c) x^2(y-z)+y^2(z-x)+z^2(x-y) I could only begin c) with expanding out the whole expression to: x^2(y) - x^2(z) + y^2(