What is factor 27m^3n^3-1 ?

The solution to factor 27m^3n^3-1 is (3mn-1)(9m^2n^2+3mn+1)

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factor 27m^3n^3-1

factor

27 m^{3} n^{3} - 1

(3 mn - 1) (9 m^{2} n^{2} + 3 mn + 1)

Solution steps

27 m^{3} n^{3} - 1

Apply exponent rules

= (3 mn)^{3} - 1^{3}

Apply Difference of Cubes Formula:

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

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

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

Simplify

(3 mn)^{2} + 3 mn + 1^{2} : 9 m^{2} n^{2} + 3 mn + 1

= (3 mn - 1) (9 m^{2} n^{2} + 3 mn + 1)

8 y - (- 8 y)

\frac{1}{10} + 1

3 a^{2} b - 75 b^{3}

(7 - 4 i) + (2 - 3 i)

1 - 125 a^{9} y^{9}

What is factor 27m^3n^3-1 ?
The solution to factor 27m^3n^3-1 is (3mn-1)(9m^2n^2+3mn+1)