Question

Factorise
x³-8y³-27z³-18xyz
if u know please answer it
using complete steps​

Answer 1

Answer:

${x}^{3} - {8y}^{3} - {27z}^{3} - 18xyz \\ \\ = > (x - 2y - 3z)( {x}^{2} + {4y}^{2} + {9z}^{2} + 2xy - 6yz + 3xz)$

Explanation:

To remember that :

${x}^{3} + {y}^{3} + {z}^{3} - 3xyz \\ \\ = > (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - xz)$

Given that:

${x}^{3} - {8y}^{3} - {27z}^{3} - 18xyz$

here we have to take it in the structure of x^3 + y^3 + z^3 - 3xyz

Now we can get :

${(x)}^{3} + {( - 2y)}^{3} + {( - 3z)}^{3} - 3.x.( - 2y).( - 3z) \\ \\ = > (x + ( - 2y) + ( - 3z))( {(x)}^{2} + {( - 2y)}^{2} + {( - 3z)}^{2} - x.( - 2y) - ( - 2y)( - 3z) - ( - 3z).x) \\ \\ = > (x - 2y - 3z)( {x}^{2} + {4y}^{2} + {9 z }^{2} + 2xy - 6yz + 3xz)$

here is your answer . hope it helps .