What is factor 512x^3-729y^3 ?

The solution to factor 512x^3-729y^3 is (8x-9y)(64x^2+72xy+81y^2)

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factor 512x^3-729y^3

factor

512 x^{3} - 729 y^{3}

(8 x - 9 y) (64 x^{2} + 72 x y + 81 y^{2})

Solution steps

512 x^{3} - 729 y^{3}

Apply exponent rules

= (8 x)^{3} - (9 y)^{3}

Apply Difference of Cubes Formula:

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

(8 x)^{3} - (9 y)^{3} = (8 x - 9 y) ((8 x)^{2} + 8 x \cdot 9 y + (9 y)^{2})

= (8 x - 9 y) ((8 x)^{2} + 8 x \cdot 9 y + (9 y)^{2})

Simplify

(8 x)^{2} + 8 x \cdot 9 y + (9 y)^{2} : 64 x^{2} + 72 x y + 81 y^{2}

= (8 x - 9 y) (64 x^{2} + 72 x y + 81 y^{2})

\frac{1}{4} (2)^{2}

- 38 - 200

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

∣ x + 1 ∣ + 4 = 3

\frac{- 8 - 9 i}{- 4 i}

What is factor 512x^3-729y^3 ?
The solution to factor 512x^3-729y^3 is (8x-9y)(64x^2+72xy+81y^2)