What is factor x^3y^3-2xy-1 ?

The solution to factor x^3y^3-2xy-1 is (xy+1)(x^2y^2-xy-1)

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factor x^3y^3-2xy-1

factor

x^{3} y^{3} - 2 x y - 1

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

Solution steps

x^{3} y^{3} - 2 x y - 1

Rewrite

x^{3} y^{3}

(x y)^{3}

= (x y)^{3} - 2 x y - 1

Use the rational root theorem

a_{0} = 1, a_{n} = 1

The dividers of

a_{0} : 1,

The dividers of

a_{n} : 1

Therefore, check the following rational numbers:

\pm \frac{1}{1}

- \frac{1}{1}

is a root of the expression, so factor out

x y + 1

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

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

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

Simplify

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

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

- \frac{17 ( π )}{12} - 4 (π)

e^{4} (3)

4 π m^{3} + 12 πm n^{2} + 9 n^{4} π

4 x^{2} - 1

m^{6} n^{3} + p^{3} q^{3}

What is factor x^3y^3-2xy-1 ?
The solution to factor x^3y^3-2xy-1 is (xy+1)(x^2y^2-xy-1)