What is factor 512x^3-27y^3 ?

The solution to factor 512x^3-27y^3 is (8x-3y)(64x^2+24xy+9y^2)

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factor 512x^3-27y^3

factor

512 x^{3} - 27 y^{3}

(8 x - 3 y) (64 x^{2} + 24 x y + 9 y^{2})

Solution steps

512 x^{3} - 27 y^{3}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(8 x)^{2} + 8 x \cdot 3 y + (3 y)^{2} : 64 x^{2} + 24 x y + 9 y^{2}

= (8 x - 3 y) (64 x^{2} + 24 x y + 9 y^{2})

- 24 + (- 19) \cdot x^{37}

\frac{( 7 + ( \frac{5}{7} \cdot x ) )}{( \frac{7}{x} )}

(i) (a \cdot b^{3})^{7} \cdot (\frac{a}{b})^{34}

a^{2} m^{4} n^{8} - 144

\frac{6}{n} + \frac{2}{( n + 1 )}

What is factor 512x^3-27y^3 ?
The solution to factor 512x^3-27y^3 is (8x-3y)(64x^2+24xy+9y^2)