Verify x^3 × y^3 =(x+y)(x^2-xy + y^3)

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Solution

To proove x3 + y3 = (x + y) ( x2 – xy + y2)

Since (x+y)3 = x3 +y3 + 3xy(x + y)

⇒ x3+ y3 = (x+y)3 - 3xy(x + y)

⇒ x3+ y3 = (x+y) [(x+y)2 - 3xy]

⇒ x3 + y3= (x+y) [x2 + y2 + 2xy - 3xy]

⇒ x3 + y3 = (x+y) (x2 + y2 -xy)

Hence prooved

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Similar questions

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

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

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