What is factor 27x^3y^3-64z^3 ?

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

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factor 27x^3y^3-64z^3

factor

27 x^{3} y^{3} - 64 z^{3}

(3 x y - 4 z) (9 x^{2} y^{2} + 12 x yz + 16 z^{2})

Solution steps

27 x^{3} y^{3} - 64 z^{3}

Rewrite

27 x^{3} y^{3}

(3 x y)^{3}

Rewrite

64 z^{3}

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

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

4 a^{2} - 1 - a^{2} + 4 a

25

5 (a)^{2}

a + (- b) + c

x^{2} + x + y - z - (y - z)^{2}

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