What is factor 27x^3-8a^3b^6 ?

The solution to factor 27x^3-8a^3b^6 is (3x-2ab^2)(9x^2+6ab^2x+4a^2b^4)

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factor 27x^3-8a^3b^6

factor

27 x^{3} - 8 a^{3} b^{6}

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

Solution steps

27 x^{3} - 8 a^{3} b^{6}

Rewrite

27 x^{3}

(3 x)^{3}

Rewrite

8 a^{3} b^{6}

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

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(3 x - 2 a b^{2}) ((3 x)^{2} + 3 x \cdot 2 a b^{2} + (2 a b^{2})^{2}) : (3 x - 2 a b^{2}) (9 x^{2} + 6 a b^{2} x + 4 a^{2} b^{4})

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

- x e^{- t} + e^{- t}

5 - 3 (ln (30))

3 x 3 + 3 x 2 - 2 x - 3

3 w^{3} + 5 w^{3} + 3 w + 5

7 x + x z - 21 y - 3 yz

What is factor 27x^3-8a^3b^6 ?
The solution to factor 27x^3-8a^3b^6 is (3x-2ab^2)(9x^2+6ab^2x+4a^2b^4)