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

Question

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

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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})

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Text solutionVerified

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

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Question Text	Verify: (i) $x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$ (ii) $x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$
Answer Type	Text solution:1
Upvotes	150