+0  
 
0
283
1
avatar

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

Guest Feb 12, 2015

Best Answer 

 #1
avatar+92781 
+5

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
 #1
avatar+92781 
+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

19 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.