What is factor 216x^3y^3-343z^3 ?

The solution to factor 216x^3y^3-343z^3 is (6xy-7z)(36x^2y^2+42xyz+49z^2)

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factor 216x^3y^3-343z^3

factor

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

(6 x y - 7 z) (36 x^{2} y^{2} + 42 x yz + 49 z^{2})

Solution steps

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

Rewrite

216 x^{3} y^{3}

(6 x y)^{3}

Rewrite

343 z^{3}

(7 z)^{3}

= (6 x y)^{3} - (7 z)^{3}

Apply Difference of Cubes Formula:

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

(6 x y)^{3} - (7 z)^{3} = (6 x y - 7 z) ((6 x y)^{2} + 7 z 6 x y + (7 z)^{2})

= (6 x y - 7 z) ((7 z)^{2} + 7 z 6 x y + (6 x y)^{2})

Simplify

(6 x y - 7 z) ((6 x y)^{2} + 7 z \cdot 6 x y + (7 z)^{2}) : (6 x y - 7 z) (36 x^{2} y^{2} + 42 x yz + 49 z^{2})

= (6 x y - 7 z) (36 x^{2} y^{2} + 42 x yz + 49 z^{2})

2 a x - 3 n x + 4 a y - 6 n y

cos (2 t) d (t) + 4 e^{- 2 t}

- 9 + sin^{2} (θ)

5^{2} + 9 t - 18

(x^{2} + 6) + 9

What is factor 216x^3y^3-343z^3 ?
The solution to factor 216x^3y^3-343z^3 is (6xy-7z)(36x^2y^2+42xyz+49z^2)