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

Open in App

Solution

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

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

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

Suggest Corrections

Similar questions

x^{3} + y^{3} = (x + y) (x^{2} + x y + y^{2})

(i) x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2}) (i i) x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

x^{3} + y^{3} - (x + y) (x^{2} - x y + y^{2})

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

Join BYJU'S Learning Program