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Question

Verify: 
(i) $$x^3+y^3=(x+y)(x^2-xy+y^2)$$ 
(ii) $$x^3-y^3=(x-y)(x^2+xy+y^2)$$


Solution

To verify put $$x=1$$ and $$y=2$$ in given equations, and check wheater LHS and RHS are equal.

(i) $$x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})$$
LHS: $$x^{3}+y^{3}=$$ $$1^{3}+2^{3}$$ $$=9$$
RHS: $$=(x+y)(x^{2}-xy+y^{2})$$ $$=(1+2)(1^{2}-1.2+2^{2})$$ $$=9$$
verified

(ii) $$x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$$
LHS:$$x^{3}-y^{3}=$$ $$1^{3}-2^{3}$$ $$=-7$$
RHS:$$(x-y)(x^{2}+xy+y^{2})$$$$=(1-2)(1^{2}+1.2+2^{2})$$ $$=-7$$
It is verified 

Mathematics
RS Agarwal
Standard IX

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