Question

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

• A. -2880
• B. 2880
• C. 3880
• D. 4880

Answer 1

The correct option is C

3880

Given that $2x-3y$ = 10.
Cubing on both sides, we get
$(2x-3y{)}^3$ = ${10}^3$

Using the identity, $(a-b{)}^3=a^3-b^3-3ab(a-b)$

$(2x-3y{)}^3=(2x{)}^3-(3y{)}^3-3(2x\left)\right(3y\left)\right(2x-3y)$

$\Rightarrow$$8x^3-27y^3-3\left(2x\right)\left(3y\right)(2x-3y)$ = 1000

Given that $xy=16$.

$\Rightarrow$ $8x^3-27y^3-18\left(16\right)\left(10\right)$ = 1000

$\Rightarrow 8x^3-27y^3-2880$ = 1000

$\Rightarrow 8x^3-27y^3$ = 3880