What is factor x^4+y^4-2x^2y^2 ?

The solution to factor x^4+y^4-2x^2y^2 is (x+y)^2(x-y)^2

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factor x^4+y^4-2x^2y^2

factor

x^{4} + y^{4} - 2 x^{2} y^{2}

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

Solution steps

x^{4} + y^{4} - 2 x^{2} y^{2}

Group by common factors

= x^{4} - 2 x^{2} y^{2} + y^{4}

Break the expression into groups

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

Factor out

x^{2}

from

x^{4} - x^{2} y^{2} : x^{2} (x^{2} - y^{2})

Factor out

- y^{2}

from

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

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

Factor out common term

x^{2} - y^{2}

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

Factor

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

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

Factor

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

= (x + y) (x - y) (x + y) (x - y)

Simplify

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

3 x^{2} + x y - 10 y^{2}

(- 3 a^{2})^{4}

\frac{4 x ^{2} - 4 y ^{2}}{x ^{2} - 3 x y - 4 y ^{2}}

(\frac{2}{3 x + 3 y})^{3}

(x + 2 y)^{3} - 1

What is factor x^4+y^4-2x^2y^2 ?
The solution to factor x^4+y^4-2x^2y^2 is (x+y)^2(x-y)^2