What is factor 27m^{12}-64n^9 ?

The solution to factor 27m^{12}-64n^9 is (3m^4-4n^3)(9m^8+12m^4n^3+16n^6)

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factor 27m^{12}-64n^9

factor

27 m^{12} - 64 n^{9}

(3 m^{4} - 4 n^{3}) (9 m^{8} + 12 m^{4} n^{3} + 16 n^{6})

Solution steps

27 m^{12} - 64 n^{9}

Apply exponent rules

= (3 m^{4})^{3} - (4 n^{3})^{3}

Apply Difference of Cubes Formula:

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

(3 m^{4})^{3} - (4 n^{3})^{3} = (3 m^{4} - 4 n^{3}) ((3 m^{4})^{2} + 3 m^{4} \cdot 4 n^{3} + (4 n^{3})^{2})

= (3 m^{4} - 4 n^{3}) ((3 m^{4})^{2} + 3 m^{4} \cdot 4 n^{3} + (4 n^{3})^{2})

Simplify

(3 m^{4})^{2} + 3 m^{4} \cdot 4 n^{3} + (4 n^{3})^{2} : 9 m^{8} + 12 m^{4} n^{3} + 16 n^{6}

= (3 m^{4} - 4 n^{3}) (9 m^{8} + 12 m^{4} n^{3} + 16 n^{6})

\frac{1}{2} x + 3 = 2

710 \cdot (0.6 - x) (0.06 - x) - x = 0

x^{2} + 10 x + 100

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

s^{2} - 6 s + 9

What is factor 27m^{12}-64n^9 ?
The solution to factor 27m^{12}-64n^9 is (3m^4-4n^3)(9m^8+12m^4n^3+16n^6)