Lösung 2.1:1g

The expression in the exercise is of the form \displaystyle (a-b)^2 , where \displaystyle a=y^2 and \displaystyle b=3x^2 . With the help of the aquaring rule \displaystyle (a-b)^2 =a^2 -2ab +b^2 , we have

\displaystyle \begin{align} \qquad (y^2-3x^3)^2 &= (y^2)^2 -2y^2\cdot 3x^3 +(3x^3)^2 \\ &= y^{2\cdot 2} -6x^3y^2 +3^2x^{3\cdot 2}\\ &= y^4 -6x^3y^2 +9x^6\\ &= 9x^6 -6x^3y^2 +y^4 \end{align}