i We know that x y 3 x3 y3 3xy x y x3 y3 x y 3 3xy x y x3 y3 x y x y 2 3xy Taking x y common x3 y3 x y x2 y2 2xy 3xy x3 y3 x y x2 y2 xy ii We know that x y 3 x3 y3 3xy x y x3 y3 x y 3 3xy x y x3 y3 x y x y 2 3xy Taking x y common x3 y3 x y x2 y2 2xy 3xy x3 y3 x y x2 y2 xy

Verify:x^3+y^3

x³ + y³ = (x + y)(x² - xy + y²)

x³ - y³ = (x - y)(x² + xy + y²)

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(i) We know that,

(x + y)³ = x³ + y³ + 3xy (x + y)

= x³ + y³ = (x + y)³ – 3xy (x + y)

= x³ + y³ = (x + y) [(x + y)² – 3xy)

{Taking (x + y) common}

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

= x³ + y³ = (x + y) (x² + y² – xy)

(ii) We know that,

(x - y)³ = x³ - y³ - 3xy (x - y)

= x³ - y³ = (x - y)³ + 3xy (x - y)

= x³ + y³ = (x - y) [(x - y)² + 3xy)

{Taking (x + y) common}

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

= x³ - y³ = (x - y) (x² + y² + xy)

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Verify:x^3+y^3

x3 + y3 = (x + y)(x2 - xy + y2) x3 - y3 = (x - y)(x2 + xy + y2)

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x³ + y³ = (x + y)(x² - xy + y²)

x³ - y³ = (x - y)(x² + xy + y²)