Question

If $2x+3y=10$ and $xy=2$, the value of $8x^3+27y^{3}isequalto$

• A. $680$
• B. $640$
• C. $520$
• D. $740$

Answer 1

The correct option is B $640$

It is given that $2x+3y=5$
Using the identity we have
$a^3+b^3=(a+b{)}^3-3ab(a+b)$
Taking a = 2x and b = 3y we get
$(2x{)}^3+(3y{)}^3=(2x+3y{)}^3-3(2x\left)\right(3y\left)\right(2x+3y)$
$8x^3+27y^3=(2x+3y{)}^3-3(2x\left)\right(3y\left)\right(2x+3y)$
$8x^3+27y^3={10}^3-3\left(2x\right)\left(3y\right)\left(10\right)$
$8x^3+27y^3=1000-180xy$
$8x^3+27y^3=1000-180\left(2\right)$
$8x^3+27y^3=1000-360$
$8x^3+27y^3=640$