What is factor 27x^{12m}+64y^{9n} ?

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

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factor 27x^{12m}+64y^{9n}

factor

27 x^{12 m} + 64 y^{9 n}

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

Solution steps

27 x^{12 m} + 64 y^{9 n}

Rewrite

27 x^{12 m}

(3 x^{4 m})^{3}

Rewrite

64 y^{9 n}

(2^{2} y^{3 n})^{3}

= (3 x^{4 m})^{3} + (2^{2} y^{3 n})^{3}

Apply Sum of Cubes Formula:

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

(3 x^{4 m})^{3} + (2^{2} y^{3 n})^{3} = (3 x^{4 m} + 2^{2} y^{3 n}) ((3 x^{4 m})^{2} - 3 x^{4 m} 2^{2} y^{3 n} + (2^{2} y^{3 n})^{2})

= (3 x^{4 m} + 2^{2} y^{3 n}) ((3 x^{4 m})^{2} - 3 x^{4 m} 2^{2} y^{3 n} + (2^{2} y^{3 n})^{2})

Simplify

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

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

3 sin^{2} (x) - 11 sin (x) + 6

(x - 1)^{3} + (y + 3)^{3}

(3 x - 2) - (2 x^{3})

\frac{2 x - 8}{x ^{2} - 16}

g (f) = 3 d e f - 8

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