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Find the H.C.F of(x2+y2)(x2+2xy+y2),(x2-y2)3 and (x6-y6

Guest Feb 12, 2015

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 #1
avatar+92196 
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Find the H.C.F of(x2+y2)(x2+2xy+y2),(x2-y2)3 and (x6-y6

 

$$\\(x^2+y^2)(x^2+2xy+y^2)\\
=(x^2+y^2)(x+y)^2\qquad (1)\\\\\\
(x^2-y^2)^3\\
=(x-y)^3(x+y)^3\qquad (2)\\\\\\
(x^6-y^6)=(x^3-y^3)(x^3+y^3)\\
=(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)\qquad(3)\\\\\\
(x^2+y^2)(x+y)^2\qquad (1)\\
(x-y)^3(x+y)^3\qquad (2)\\
(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)\qquad(3)\\\\\\
HCF= x+y$$

 

I think that is correct. 

Melody  Feb 12, 2015
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1+0 Answers

 #1
avatar+92196 
+5
Best Answer

Find the H.C.F of(x2+y2)(x2+2xy+y2),(x2-y2)3 and (x6-y6

 

$$\\(x^2+y^2)(x^2+2xy+y^2)\\
=(x^2+y^2)(x+y)^2\qquad (1)\\\\\\
(x^2-y^2)^3\\
=(x-y)^3(x+y)^3\qquad (2)\\\\\\
(x^6-y^6)=(x^3-y^3)(x^3+y^3)\\
=(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)\qquad(3)\\\\\\
(x^2+y^2)(x+y)^2\qquad (1)\\
(x-y)^3(x+y)^3\qquad (2)\\
(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)\qquad(3)\\\\\\
HCF= x+y$$

 

I think that is correct. 

Melody  Feb 12, 2015

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