Derive the cubic polynomial: $x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$

Open in App

Solution

$x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$
First take R.H.S
$(x - y) (x^{2} + x y + y^{2})$
To multiply two polynomials, we multiply each monomial of one polynomial (with its sign) by each monomial (with its sign) of the other polynomial.
$=$ $x . x^{2} + x^{2} y + x . y^{2} - y . x^{2} - x . y^{2} - y . y^{2}$
$=$ $x^{3} + x^{2} y + x y^{2} - x^{2} y - x y^{2} - y^{3}$
$=$ $x^{3} - y^{3}$
So, L.H.S $=$ R.H.S
$x^{3} - y^{3} = x^{3} - y^{3}$
Hence, $x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$ is derived.

Suggest Corrections

Similar questions

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

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

(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})

Join BYJU'S Learning Program