What is factor (x^8y^8)-1 ?

The solution to factor (x^8y^8)-1 is (x^4y^4+1)(x^2y^2+1)(xy+1)(xy-1)

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factor (x^8y^8)-1

factor

(x^{8} y^{8}) - 1

(x^{4} y^{4} + 1) (x^{2} y^{2} + 1) (x y + 1) (x y - 1)

Solution steps

(x^{8} y^{8}) - 1

Remove parentheses:

(a) = a

= x^{8} y^{8} - 1

Rewrite

x^{8} y^{8} - 1

(x^{4} y^{4})^{2} - 1

= (x^{4} y^{4})^{2} - 1

Apply Difference of Two Squares Formula:

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

(x^{4} y^{4})^{2} - 1 = (x^{4} y^{4} + 1) (x^{4} y^{4} - 1)

= (x^{4} y^{4} + 1) (x^{4} y^{4} - 1)

Factor

x^{4} y^{4} - 1 : (x^{2} y^{2} + 1) (x y + 1) (x y - 1)

= (x^{4} y^{4} + 1) (x^{2} y^{2} + 1) (x y + 1) (x y - 1)

x^{2} - 16 x + (- 8)

e^{10 x^{2} + 4 y^{2} + 8}

6 (2 p + q)^{2} + (2 p + q)^{- 2}

x e^{2} + 2 x

27 y^{3} - 8 y^{3}

What is factor (x^8y^8)-1 ?
The solution to factor (x^8y^8)-1 is (x^4y^4+1)(x^2y^2+1)(xy+1)(xy-1)