9.(i) Verify:

   (i)    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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