Verify : $x^{3}$ + $y^{3}$ = (x + y) ( $x^{2}$ – xy + $y^{2}$ )

Open in App

Solution

To proove $x^{3}$ + $y^{3}$ = (x + y) ( $x^{2}$ – xy + $y^{2}$ )

Since ${(x + y)}^{3}$ = $x^{3}$ + $y^{3}$ + 3xy(x + y)

⇒ $x^{3}$ + $y^{3}$ = ${(x + y)}^{3}$ - 3xy(x + y)

⇒ $x^{3}$ + $y^{3}$ = (x+y) [ ${(x + y)}^{2}$ - 3xy]

⇒ $x^{3}$ + $y^{3}$ = (x+y) [ $x^{2}$ + $y^{2}$ + 2xy - 3xy]

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

Hence prooved

Suggest Corrections

Similar questions

(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})

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

Join BYJU'S Learning Program