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# the H.C.F

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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

#1
+91972
+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
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#1
+91972
+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

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