Solve (x^(6)-y^(6))

Evaluate

x^{6} - y^{6}

Calculate

x^{6} + x^{5} y - x^{3} y^{3} - x^{2} y^{4} - x^{5} y - x^{4} y^{2} + x^{2} y^{4} + x y^{5} + y^{2} x^{4} + y^{3} x^{3} - y^{5} x - y^{6}

Rewrite the expression

x^{2} \times x^{4} + x^{2} \times x^{3} y - x^{2} \times x y^{3} - x^{2} y^{4} - x y x^{4} - x y x^{3} y + x y x y^{3} + x y \times y^{4} + y^{2} x^{4} + y^{2} x^{3} y - y^{2} x y^{3} - y^{2} \times y^{4}

Factor out x^{2} from the expression

x^{2} (x^{4} + x^{3} y - x y^{3} - y^{4}) - x y x^{4} - x y x^{3} y + x y x y^{3} + x y \times y^{4} + y^{2} x^{4} + y^{2} x^{3} y - y^{2} x y^{3} - y^{2} \times y^{4}

Factor out - x y from the expression

x^{2} (x^{4} + x^{3} y - x y^{3} - y^{4}) - x y (x^{4} + x^{3} y - x y^{3} - y^{4}) + y^{2} x^{4} + y^{2} x^{3} y - y^{2} x y^{3} - y^{2} \times y^{4}

Factor out y^{2} from the expression

x^{2} (x^{4} + x^{3} y - x y^{3} - y^{4}) - x y (x^{4} + x^{3} y - x y^{3} - y^{4}) + y^{2} (x^{4} + x^{3} y - x y^{3} - y^{4})

Factor out x^{4} + x^{3} y - x y^{3} - y^{4} from the expression

(x^{2} - x y + y^{2}) (x^{4} + x^{3} y - x y^{3} - y^{4})

Factor the expression

More Steps

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

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

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

Solution

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