What is factor 64m^6-729n^6 ?

The solution to factor 64m^6-729n^6 is (2m+3n)(4m^2-6mn+9n^2)(2m-3n)(4m^2+6mn+9n^2)

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factor 64m^6-729n^6

factor

64 m^{6} - 729 n^{6}

(2 m + 3 n) (4 m^{2} - 6 mn + 9 n^{2}) (2 m - 3 n) (4 m^{2} + 6 mn + 9 n^{2})

Solution steps

64 m^{6} - 729 n^{6}

64 m^{6} = (8 m^{3})^{2}

729 n^{6} = (27 n^{3})^{2}

= (8 m^{3})^{2} - (27 n^{3})^{2}

Apply Difference of Two Squares Formula:

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

(8 m^{3})^{2} - (27 n^{3})^{2} = (8 m^{3} + 27 n^{3}) (8 m^{3} - 27 n^{3})

= (8 m^{3} + 27 n^{3}) (8 m^{3} - 27 n^{3})

Factor

8 m^{3} + 27 n^{3} : (2 m + 3 n) (4 m^{2} - 6 mn + 9 n^{2})

= (2 m + 3 n) (4 m^{2} - 6 mn + 9 n^{2}) (8 m^{3} - 27 n^{3})

Factor

8 m^{3} - 27 n^{3} : (2 m - 3 n) (4 m^{2} + 6 mn + 9 n^{2})

= (2 m + 3 n) (4 m^{2} - 6 mn + 9 n^{2}) (2 m - 3 n) (4 m^{2} + 6 mn + 9 n^{2})

a^{4} + 16 a^{2} + 64

(3 a + 5 b)^{3}

x^{2} - ln (x^{2}) + k

(a + b)^{11}

\frac{1}{2} x \frac{\frac{( v ^{2} + v ^{3} )}{3}}{2} x (v^{18} + v^{3})

What is factor 64m^6-729n^6 ?
The solution to factor 64m^6-729n^6 is (2m+3n)(4m^2-6mn+9n^2)(2m-3n)(4m^2+6mn+9n^2)