What is factor x^3y^3+x^2y^2+4 ?

The solution to factor x^3y^3+x^2y^2+4 is (xy+2)(x^2y^2-xy+2)

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factor x^3y^3+x^2y^2+4

factor

x^{3} y^{3} + x^{2} y^{2} + 4

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

Solution steps

x^{3} y^{3} + x^{2} y^{2} + 4

Rewrite

x^{3} y^{3}

(x y)^{3}

Rewrite

x^{2} y^{2}

(x y)^{2}

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

Use the rational root theorem

a_{0} = 4, a_{n} = 1

The dividers of

a_{0} : 1, 2, 4,

The dividers of

a_{n} : 1

Therefore, check the following rational numbers:

\pm \frac{1 , 2 , 4}{1}

- \frac{2}{1}

is a root of the expression, so factor out

x y + 2

= (x y + 2) \frac{( x y ) ^{3} + ( x y ) ^{2} + 4}{x y + 2}

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

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

Simplify

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

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

125 x^{3} y^{6} z^{12} - d^{9}

2^{\frac{1}{2}} \cdot 725 + 1200

in (2.3)

I m (z)^{3}

3 x^{2 + 4 x - 5}

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