Answers

2014-10-18T19:59:10+05:30
X^8-y^8
⇒(x^4)^2-(y^4)^2
⇒(x^4+y^4)(x^4-y^4)
⇒(x^4+y^4)[(x^2)^2-(y^2)^2]
⇒(x^4+y^4)(x^2+y^2)(x^2-y^2)
⇒(x^4+y^4)(x^2+y^2)(x+y)(x-y)
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2014-10-18T21:02:23+05:30
X^8-y^8
we can write x^8 as (x^4)^2
⇒(x^4)^2-(y^4)^2
It is in the form of a^2-b^2=(a+b)(a-b)
Here we have a=x^4 and b=y^4
⇒(x^4+y^4)(x^4-y^4)
⇒(x^4+y^4)[(x^2)^2-(y^2)^2]
Again it is in the form of a^2-b^2=(a+b)(a-b)
Here a=x^2 and b=y^2
⇒(x^4+y^4)(x^2+y^2)(x^2-y^2)
Applying A^2-b^2 formulae for x^2-y^2
Formulae for it is ((a-b)(a+b))
Here a=x and b=y
⇒(x^4+y^4)(x^2+y^2)(x+y)(x-y)
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