What is factor 343x^3y^3-64z^3 ?

The solution to factor 343x^3y^3-64z^3 is (7xy-4z)(49x^2y^2+28xyz+16z^2)

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factor 343x^3y^3-64z^3

factor

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

(7 x y - 4 z) (49 x^{2} y^{2} + 28 x yz + 16 z^{2})

Solution steps

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

Rewrite

343 x^{3} y^{3}

(7 x y)^{3}

Rewrite

64 z^{3}

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

= (7 x y)^{3} - (2^{2} z)^{3}

Apply Difference of Cubes Formula:

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

(7 x y)^{3} - (2^{2} z)^{3} = (7 x y - 2^{2} z) ((7 x y)^{2} + 2^{2} z 7 x y + (2^{2} z)^{2})

= (7 x y - 2^{2} z) ((2^{2} z)^{2} + 2^{2} z 7 x y + (7 x y)^{2})

Simplify

(7 x y - 2^{2} z) ((7 x y)^{2} + 2^{2} z \cdot 7 x y + (2^{2} z)^{2}) : (7 x y - 4 z) (49 x^{2} y^{2} + 28 x yz + 16 z^{2})

= (7 x y - 4 z) (49 x^{2} y^{2} + 28 x yz + 16 z^{2})

x^{2} - 13 + 30

x^{2} - 13 + 36

x y - z - 5 z^{2} + 5 x yz

- e^{x} sin (x) - e^{x} cos (x)

(2) (3 + 3) + 3

What is factor 343x^3y^3-64z^3 ?
The solution to factor 343x^3y^3-64z^3 is (7xy-4z)(49x^2y^2+28xyz+16z^2)