Q= If x + y = a
and x^2 + y^2 = b^2
find an expression for ( x^2 - y^2)^2 in terms of a and b
cheers for the help
$\displaystyle \begin{array}{lrcl}
{} & x+y &=& a\\\\
\Rightarrow & x^2+2xy+y^2 &=& a^2\\\\
\Rightarrow & 2xy &=& a^2-b^2\\\\
\Rightarrow & 4x^2y^2 &=& (a^2-b^2)^2
\end{array}$
Now use the formula $\displaystyle (x^2-y^2)^2=(x^2+y^2)^2-4x^2y^2$ to finish off.