What is factor 27a^3b^6+c^3 ?

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

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factor 27a^3b^6+c^3

factor

27 a^{3} b^{6} + c^{3}

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

Solution steps

27 a^{3} b^{6} + c^{3}

Rewrite

27 a^{3} b^{6}

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

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

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

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

5 x^{2} - 2 x^{2} - 10 x + 4

2 - (2 \cdot ln (2))

\cdot m + y m + n \cdot + n y

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

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

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