Question

If 2x -3y -4z=0 ,then find 8x^3-27y^3- 64z^3

Answer 1

Answer:

$8x^3-27y^3-64z^3=72xyz$

Step-by-step explanation:

If 2x -3y -4z=0 ,then find 8x^3-27y^3- 64z^3

Given:

$2x-3y-4z=0$ .........(1)

$2x=3y+4z$

cubing on both sides, we get

$(2x)^3=(3y+4z)^3$

using

$\boxed{(a+b)^3=a^3+b^3+3ab(a+b)}$

$\implies\:8x^3=(3y)^3+(4z)^3+3(3y)(4z)(3y+4z)$

$\implies\:8x^3=27y^3+64z^3+3(3y)(4z)(2x)$ ( using (1) )

$\implies\:8x^3=27y^3+64z^3+72xyz$ ( using (1) )

$\implies\:\boxed{8x^3-27y^3-64z^3=72xyz}$