Question

$if \: 2x - 3y - 4z = 0 \: then \: find \: \: 8x {3 - 27y {3 - 64z {3}^{} }^{} }^{}$
Hi​

Answer 1

Answer:

$8 {x}^{3} - 27 {y}^{3} - 64 {z}^{3} \\ = {(2x)}^{3} + { ( - 3y)}^{3} + {( - 4z)}^{3} \\ \\ let \: consider \\ 2x = a \\ - 3y = b \\ - 4z = c \\ \\ = {a}^{3} + {b}^{3} + {c}^{3} - 3abc + 3abc \\ = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca) + 3abc \\ = 3abc \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: |a + b + c = 0 \\ = 3 \times 2x \times ( - 3y) \times ( - 4z) \\ = 72xyz|$