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

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

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

factor

x^{4} - 10 x^{2} 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}

\frac{1}{3 + 2}

\frac{7 x}{x ^{2} - 4} + \frac{2}{x + 2}

\frac{\frac{2 b - 10}{3}}{\frac{b - 5}{9}}

tan^{2} (θ) - sec^{2} (θ)

\frac{6 x ^{2} + 15 x}{12 x ^{2} - 75}

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