What is factor m^3n^3x^3+1 ?

The solution to factor m^3n^3x^3+1 is (mnx+1)(m^2n^2x^2-mnx+1)

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factor m^3n^3x^3+1

factor

m^{3} n^{3} x^{3} + 1

(mn x + 1) (m^{2} n^{2} x^{2} - mn x + 1)

Solution steps

m^{3} n^{3} x^{3} + 1

Rewrite

m^{3} n^{3} x^{3}

(mn x)^{3}

= (mn x)^{3} + 1

Rewrite

1

1^{3}

= (mn x)^{3} + 1^{3}

Apply Sum of Cubes Formula:

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

(mn x)^{3} + 1^{3} = (mn x + 1) ((mn x)^{2} - mn x + 1)

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

Simplify

(mn x + 1) ((mn x)^{2} - mn x + 1) : (mn x + 1) (m^{2} n^{2} x^{2} - mn x + 1)

= (mn x + 1) (m^{2} n^{2} x^{2} - mn x + 1)

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

(2) e^{2}

2 x (3 - 2 x)^{'} + 4 (x - 1)^{'}

[- 15.15]

\frac{x ^{2} + x - 2}{x - 1}

What is factor m^3n^3x^3+1 ?
The solution to factor m^3n^3x^3+1 is (mnx+1)(m^2n^2x^2-mnx+1)