If $2 x - 3 y = 4$ , the value of $8 x^{3} - 27 y^{3} - 72 x y$ is

$32$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$16$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$128$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$64$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
$64$

Explanation for correct answer:
Using identities and finding the value of $8 x^{3} - 27 y^{3} - 72 x y$ :
(Identity used $a^{3} - b^{3} = {(a - b)}^{3} + 3 a b (a - b)$ ).
$8 x^{3} - 27 y^{3} - 72 x y = {(2 x)}^{3} - {(3 y)}^{3} - 72 x y$
$= {(2 x - 3 y)}^{3} + 3 \times 2 x \times 3 y \times (2 x - 3 y) - 72 x y$
$= 4^{3} + 3 \times 2 x \times 3 y \times 4 - 72 x y$ ( $∵$ Given $2 x - 3 y = 4$ )
$= 4^{3} + 72 x y - 72 x y$
$= 4^{3} = 64$
Hence the correct answer is (D).

Suggest Corrections

Similar questions

If $2 x - 3 y$ = 10 and $x y = 16$ ; find the value of $8 x^{3} - 27 y^{3}$

2 x + 3 y = 12

x y = 6

8 x^{3} + 27 y^{3}

If 2x+3y=13 and xy=6 find the value of 8x³+27y³.

8 x^{3} - 27 y^{3} - 2 x + 3 y :

Join BYJU'S Learning Program