Solve x^8 + 14 x^4 y^4 + y^8 - Socratic AI (ScanMath)

Evaluate

x^{8} + 14 x^{4} y^{4} + y^{8}

Calculate

x^{8} - 2 x^{7} y + 2 x^{6} y^{2} + 2 x^{5} y^{3} + x^{4} y^{4} + 2 x^{7} y - 4 x^{6} y^{2} + 4 x^{5} y^{3} + 4 x^{4} y^{4} + 2 x^{3} y^{5} + 2 x^{6} y^{2} - 4 x^{5} y^{3} + 4 x^{4} y^{4} + 4 x^{3} y^{5} + 2 x^{2} y^{6} - 2 x^{5} y^{3} + 4 x^{4} y^{4} - 4 x^{3} y^{5} - 4 x^{2} y^{6} - 2 x y^{7} + y^{4} x^{4} - 2 y^{5} x^{3} + 2 y^{6} x^{2} + 2 y^{7} x + y^{8}

Rewrite the expression

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

Factor out x^{4} from the expression

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

Factor out 2 x^{3} y from the expression

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

Factor out 2 x^{2} y^{2} from the expression

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

Factor out - 2 x y^{3} from the expression

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

Factor out y^{4} from the expression

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

Solution

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

X^8 + 14 x^4 y^4 + y^8