What is factor x^4-8x^2y^2+16y^4 ?

The solution to factor x^4-8x^2y^2+16y^4 is (x+2y)^2(x-2y)^2

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factor x^4-8x^2y^2+16y^4

factor

x^{4} - 8 x^{2} y^{2} + 16 y^{4}

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

Solution steps

x^{4} - 8 x^{2} y^{2} + 16 y^{4}

Break the expression into groups

= (x^{4} - 4 x^{2} y^{2}) + (- 4 x^{2} y^{2} + 16 y^{4})

Factor out

x^{2}

from

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

Factor out

- 4 y^{2}

from

- 4 x^{2} y^{2} + 16 y^{4} : - 4 y^{2} (x^{2} - 4 y^{2})

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

Factor out common term

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

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

Factor

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

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

Factor

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

= (x + 2 y) (x - 2 y) (x + 2 y) (x - 2 y)

Simplify

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

8 (y - x) - 2 (x - y)

(4 a + 2) (m^{2} - 9 + 2)

x^{3} + 9 x^{2} - 108

4^{- 1} + 3^{- 1}

2 \cdot 4

What is factor x^4-8x^2y^2+16y^4 ?
The solution to factor x^4-8x^2y^2+16y^4 is (x+2y)^2(x-2y)^2