What is factor 64w^6z^9-27y^3 ?

The solution to factor 64w^6z^9-27y^3 is (4w^2z^3-3y)(16w^4z^6+12w^2z^3y+9y^2)

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factor 64w^6z^9-27y^3

factor

64 w^{6} z^{9} - 27 y^{3}

(4 w^{2} z^{3} - 3 y) (16 w^{4} z^{6} + 12 w^{2} z^{3} y + 9 y^{2})

Solution steps

64 w^{6} z^{9} - 27 y^{3}

Rewrite

64 w^{6} z^{9}

(2^{2} w^{2} z^{3})^{3}

Rewrite

27 y^{3}

(3 y)^{3}

= (2^{2} w^{2} z^{3})^{3} - (3 y)^{3}

Apply Difference of Cubes Formula:

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

(2^{2} w^{2} z^{3})^{3} - (3 y)^{3} = (2^{2} w^{2} z^{3} - 3 y) ((2^{2} w^{2} z^{3})^{2} + 2^{2} w^{2} z^{3} 3 y + (3 y)^{2})

= (2^{2} w^{2} z^{3} - 3 y) ((2^{2} w^{2} z^{3})^{2} + 2^{2} w^{2} z^{3} 3 y + (3 y)^{2})

Simplify

(2^{2} w^{2} z^{3} - 3 y) ((2^{2} w^{2} z^{3})^{2} + 2^{2} w^{2} z^{3} \cdot 3 y + (3 y)^{2}) : (4 w^{2} z^{3} - 3 y) (16 w^{4} z^{6} + 12 w^{2} z^{3} y + 9 y^{2})

= (4 w^{2} z^{3} - 3 y) (16 w^{4} z^{6} + 12 w^{2} z^{3} y + 9 y^{2})

(k)^{2}

x^{2 n} + x^{n + 3} - x^{n + 1} - x^{4}

\frac{x ^{3} + 1}{x + 1}

\frac{( x - 5 ) ^{2} - 25}{x}

csc (x^{3} - 5 x)

What is factor 64w^6z^9-27y^3 ?
The solution to factor 64w^6z^9-27y^3 is (4w^2z^3-3y)(16w^4z^6+12w^2z^3y+9y^2)