Question

If $x-2y=11$ and $xy=8$ find the value of $x^3-8y^3$.

Answer 1

We know that $(a-b{)}^3=a^3-b^3-3ab(a-b)$

Now, $x-2y=11$

Cubing both sides we get

$x^3-8y^3-3\times x\times 2y(x-2y)={11}^3$

$x^3-8y^3-6xy(x-2y)=1331$

Put the values of $x-2y$ and $xy$,

$x^3-8y^3-6\times 8\times 11=1331$

$x^3-8y^3=1331+528$

$x^3-8y^3=1859$