If ω is cube root of unity the linear factors of x3 + y3 in complex number is

Question

If ω is cube root of unity the linear factors of x3 + y3 in complex number is (A) (x -y) (x - ω y)(x -ω2 y) (B) (x -y) (x + ω y)(x +ω2 y) (C) (x + y) (x + ω y)(x +ω2 y) (D) (x + y) (x - ω y)(x - ω2 y)

Tardigrade Admin · Accepted Answer

x3 + y3 = (x + y) (x2 - xy + y2) = (x + y) (x2 + (ω + ω2) xy + y2) <bR> = (x + y) (x + ω y) (x + ω2y)

Q. If $ω$ is cube root of unity the linear factors of $x^{3} + y^{3}$ in complex number is

$(x - y) (x - ω y) (x - ω^{2} y)$

$(x - y) (x + ω y) (x + ω^{2} y)$

$(x + y) (x + ω y) (x + ω^{2} y)$

$(x + y) (x - ω y) (x - ω^{2} y)$

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

Q. If ω is cube root of unity the linear factors of x3+y3 in complex number is

(x−y)(x−ωy)(x−ω2y)

(x−y)(x+ωy)(x+ω2y)

(x+y)(x+ωy)(x+ω2y)

(x+y)(x−ωy)(x−ω2y)