Question

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

Answer 1

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Answer:

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

x^3 + y^3 + 3x^2y + 3xy^2 = (x+y) (x^2+2xy+y^2)

x^3 + y^3 = (x+y)(x^2+2xy+y^2) -3x^2y -3xy^2

x^3 + y^3 = (x+y)(x^2+2xy+y^2)

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Answer 2

Step-by-step explanation:

${x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} ) \\ for \: lhs - > \\ (x + y)( {x}^{2} - xy + {y}^{2} ) \\ = > x \times ( {x}^{2} - xy + {y}^{2} ) + y \times ( {x}^{2} - xy + {y}^{2} ) \\ = > {x}^{3} - {x}^{2} y + x {y}^{2} + {x}^{2} y - x {y}^{2} + {y}^{3} \\ = > {x}^{3} + {y}^{3} = rhs \\ so \\ = > rhs= lhs \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: h.p.$