9.(ii)  Verify:

    (ii)    x^3 - y^3 = (x -y)(x^2 + xy + y^2)

Answers (1)
R Riya

We know that

(x-y)^3=x^3-y^3-3xy(x-y)

Now,

\Rightarrow x^3-y^3=(x-y)^3+3xy(x-y)

\Rightarrow x^3-y^3=(x-y)\left((x-y)^2+3xy \right )

\Rightarrow x^3-y^3=(x-y)\left(x^2+y^2-2xy+3xy \right )                                                (\because (a-b)^2=a^2+b^2-2ab)                                           

\Rightarrow x^3-y^3=(x-y)\left(x^2+y^2+xy \right )

Hence proved 

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