Question

2x-3y=4 then find the value of 8x^3-27y^3-72xy

Answer 1

HERE

2X-3Y=4

NOW

8X^3-27Y^3-72XY

=(2X)^3-(3Y)^3-72XY

=[(2X-3Y)(4X^2+6XY+3Y^2)]-72XY

=4[(2X)^2+(3Y)^2+6XY)-72XY

=4[(2X-3Y)^2+12XY+6XY)-72XY

=4(4^2+18XY)-72XY

=4(16+18XY)-72XY

=64+72XY-72XY

=64

Answer 2

Explanation:

$\bf \underline{Given-}$

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

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

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

$\bf \underline{Solution-}$

$\textsf{We have,}$

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

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

$\textsf{(2x - 3y)³ = (4)³}$

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

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

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

$\textsf{(2x - 3y)³ = (4)³}$

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

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

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

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

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

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