What is factor x^8-81y^8 ?

The solution to factor x^8-81y^8 is (x^4+9y^4)(x^2+3y^2)(x^2-3y^2)

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factor x^8-81y^8

factor

x^{8} - 81 y^{8}

(x^{4} + 9 y^{4}) (x^{2} + 3 y^{2}) (x^{2} - 3 y^{2})

Solution steps

x^{8} - 81 y^{8}

x^{8} = (x^{4})^{2}

81 y^{8} = (9 y^{4})^{2}

= (x^{4})^{2} - (9 y^{4})^{2}

Apply Difference of Two Squares Formula:

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

(x^{4})^{2} - (9 y^{4})^{2} = (x^{4} + 9 y^{4}) (x^{4} - 9 y^{4})

= (x^{4} + 9 y^{4}) (x^{4} - 9 y^{4})

Factor

x^{4} - 9 y^{4} : (x^{2} + 3 y^{2}) (x^{2} - 3 y^{2})

= (x^{4} + 9 y^{4}) (x^{2} + 3 y^{2}) (x^{2} - 3 y^{2})

(\frac{1}{2} - \frac{1}{2} i)^{- 7}

(5 a - 8)^{3}

- 5 \frac{3}{4} - 3 \frac{1}{2}

(sin (t) - cos (t))^{2}

\frac{1}{3} (x^{2} + 2)^{\frac{3}{2}}

What is factor x^8-81y^8 ?
The solution to factor x^8-81y^8 is (x^4+9y^4)(x^2+3y^2)(x^2-3y^2)