What is factor a^6b^3-27c^9 ?

The solution to factor a^6b^3-27c^9 is (a^2b-3c^3)(a^4b^2+3a^2bc^3+9c^6)

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factor a^6b^3-27c^9

factor

a^{6} b^{3} - 27 c^{9}

(a^{2} b - 3 c^{3}) (a^{4} b^{2} + 3 a^{2} b c^{3} + 9 c^{6})

Solution steps

a^{6} b^{3} - 27 c^{9}

Rewrite

a^{6} b^{3}

(a^{2} b)^{3}

Rewrite

27 c^{9}

(3 c^{3})^{3}

= (a^{2} b)^{3} - (3 c^{3})^{3}

Apply Difference of Cubes Formula:

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

(a^{2} b)^{3} - (3 c^{3})^{3} = (a^{2} b - 3 c^{3}) ((a^{2} b)^{2} + 3 c^{3} a^{2} b + (3 c^{3})^{2})

= (a^{2} b - 3 c^{3}) ((3 c^{3})^{2} + 3 c^{3} a^{2} b + (a^{2} b)^{2})

Simplify

(a^{2} b - 3 c^{3}) ((a^{2} b)^{2} + 3 c^{3} a^{2} b + (3 c^{3})^{2}) : (a^{2} b - 3 c^{3}) (a^{4} b^{2} + 3 a^{2} b c^{3} + 9 c^{6})

= (a^{2} b - 3 c^{3}) (a^{4} b^{2} + 3 a^{2} b c^{3} + 9 c^{6})

1 + 2 sin (x) - 3 sin^{2} (x)

2 m x + 3 n x - 3 n y - 2 m y

(2 u) \cdot v

\frac{x ^{2} - 3 x - 4}{x - 1}

What is factor a^6b^3-27c^9 ?
The solution to factor a^6b^3-27c^9 is (a^2b-3c^3)(a^4b^2+3a^2bc^3+9c^6)