Question

If 2x-3y=4,find the value of 8xcube -27ycube-72xy

Answer 1

2x-3y=4
cubing both sides
(2x-3y)³=(4)³
as we know
(a-b)³=a³-b³-3ab(a-b)
so,
(2x-3y)³=(4)³
8x³-27y³-3(2x)(3y)(2x-3y)=64
8x³-27y³-18xy(4) =64. (bcoz 2x-3y=4 given)
8x³-27y³-72xy=64

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

$\textsf{2x - 3y = 4}$

$\bf \underline{To\: find-}$

$\textsf{the value of 8x³ - 27y³ - 72xy = ?}$

$\bf \underline{Solution-}$

$\textsf{We have,}$

$\textsf{2x - 3y = 4}$

$\textsf{Cubing on both sides, we get}$

$\textsf{(2x - 3y)³ = (4)³}$

$\textsf{★Now, comparing the given expression with (a-b)³, we get}$

$\textsf{\: \: \: \: \: a = 2x and b = 3y.}$

$\textsf{★Using identity (a-b)³ = a³-b³-3ab(a-b), we have}$

$\textsf{(2x - 3y)³ = (4)³}$

$\sf{ \implies \: (2x {)}^{3} - (3x {)}^{3} - 3(2x)(3y)(2x - 3y) = 64}$

$\sf{ \implies \: 8 {x}^{3} - 27 {y}^{3} - 18xy(2x - 3y) = 64 }$

$[\textsf{Since, (2x - 3y) = 4 (Given)}]$

$\sf{ \implies \: 8 {x}^{3} - 27 {y}^{3} - 18xy(4) = 64 }$

$\sf{ \implies \: 8 {x}^{3} - 27 {y}^{3} - 72xy= 64 }$

$\bf \underline{Hence, the\: value\: of\: 8x³-27y³-72xy \: is\: 64.}$