Question

If 2x + 3y + z=0, then find the value of 8x³+27y³+z³.

Answer 1

Question:

If 2x + 3y + z=0, then find the value of 8x³+27y³+z³.

Given:

2x + 3y + z = 0

To find:

To find the value of 8x³+27y³+z³.

Answer:

$( {8x}^{3} + {27y}^{3} + {z}^{3} ) = \underline {\: \bold{18xyz} \: }$

Step-by-step explanation:

We know that,

a³+b³+ c³ = (a +b +c)(a²+ b²+ c²-ab-bc-ca) + 3abc

To find the value of 8x³+27y³+z³

a = 2x, b = 3y, c = z.

2x + 3y + z = 0

8x³+27y³+z³ = [(0)(a²+b²+c²-ab-bc-ca)]+ 3(2x)(3y)(z)

= [ 0 ] + 18xyz

$\boxed{( {8x}^{3} + {27y}^{3} + {z}^{3} ) = 18xyz}$