What is factor x^{12}y^{18}+1 ?

The solution to factor x^{12}y^{18}+1 is (x^4y^6+1)(x^8y^{12}-x^4y^6+1)

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factor x^{12}y^{18}+1

factor

x^{12} y^{18} + 1

(x^{4} y^{6} + 1) (x^{8} y^{12} - x^{4} y^{6} + 1)

Solution steps

x^{12} y^{18} + 1

Apply exponent rules

= (x^{4} y^{6})^{3} + 1^{3}

Apply Sum of Cubes Formula:

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

(x^{4} y^{6})^{3} + 1^{3} = (x^{4} y^{6} + 1) ((x^{4} y^{6})^{2} - x^{4} y^{6} + 1^{2})

= (x^{4} y^{6} + 1) ((x^{4} y^{6})^{2} - x^{4} y^{6} + 1^{2})

Simplify

(x^{4} y^{6})^{2} - x^{4} y^{6} + 1^{2} : x^{8} y^{12} - x^{4} y^{6} + 1

= (x^{4} y^{6} + 1) (x^{8} y^{12} - x^{4} y^{6} + 1)

5 x^{2} - 20 y^{2}

\frac{1}{2} > - 2 x + \frac{7}{2}

∣ 12 ∣

2 k^{2} - 14 k - 60

2 x^{2} - 13 x + 21 = 0

What is factor x^{12}y^{18}+1 ?
The solution to factor x^{12}y^{18}+1 is (x^4y^6+1)(x^8y^{12}-x^4y^6+1)