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

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

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

factor

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

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

Solution steps

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

Break the expression into groups

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

Factor out

x^{2}

from

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

Factor out

- 2 y^{2}

from

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

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

Factor out common term

x^{2} - 2 y^{2}

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

Apply exponent rule:

aa = a^{2}

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

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

x + 3 < 7

r^{2} + 2 rs + s^{2} - 9

4 x^{2} + 14 x + 21 = 0

(4 x^{5} - 2 x^{3} + 2 x + 3) (4 x^{5} - 2 x^{3} + 2 x + 3)

j^{2} k^{2} + 3 j k^{2}

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