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

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

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factor 8a^3-27b^6

factor

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

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

Solution steps

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

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

\frac{- 11 π}{3}

(6 x - 4) (2 x - 7)

(2 + 3 i) \cdot (4 + 5 i)

(\frac{9}{- 10}) (\frac{6}{- 7})

x^{3} - 64 y^{6}

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