What is factor x^4-10x^2*y^2+25y^4 ?

The solution to factor x^4-10x^2*y^2+25y^4 is (x^2-5y^2)^2

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factor x^4-10x^2*y^2+25y^4

factor

x^{4} - 10 x^{2} \cdot y^{2} + 25 y^{4}

(x^{2} - 5 y^{2})^{2}

Solution steps

x^{4} - 10 x^{2} y^{2} + 25 y^{4}

Break the expression into groups

= (x^{4} - 5 x^{2} y^{2}) + (- 5 x^{2} y^{2} + 25 y^{4})

Factor out

x^{2}

from

x^{4} - 5 x^{2} y^{2} : x^{2} (x^{2} - 5 y^{2})

Factor out

- 5 y^{2}

from

- 5 x^{2} y^{2} + 25 y^{4} : - 5 y^{2} (x^{2} - 5 y^{2})

= x^{2} (x^{2} - 5 y^{2}) - 5 y^{2} (x^{2} - 5 y^{2})

Factor out common term

x^{2} - 5 y^{2}

= (x^{2} - 5 y^{2}) (x^{2} - 5 y^{2})

Apply exponent rule:

aa = a^{2}

(x^{2} - 5 y^{2}) (x^{2} - 5 y^{2}) = (x^{2} - 5 y^{2})^{2}

= (x^{2} - 5 y^{2})^{2}

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

(a_{b}^{3})^{3} + 3 a - 3 b

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

\frac{0.5 x 1 0 ^{- 3}}{1 0 ^{- 6}}

(x - 3) (x - 4) + (x - 3) (x + 4)

What is factor x^4-10x^2*y^2+25y^4 ?
The solution to factor x^4-10x^2*y^2+25y^4 is (x^2-5y^2)^2