Lösung 2.1:1h

We expand the quadratic with the squaring rule \displaystyle (a+b)^2=a^2+2ab+b^2 , where \displaystyle a=5x^3 and \displaystyle b=3x^5

\displaystyle \qquad \begin{align} (5x^3 + 3x^5)^2 &= (5x^3)^2 +2\cdot 5x^3\cdot 3x^5 +(3x^5)^{2} \\ &= 5^2x^{3\cdot 2} + 2\cdot 5\cdot 3\cdot x^{3+5}+ 3^2 x^{5\cdot 2}\\ &= 25x^6 +30 x^8 +9x^{10}\\ &= 9x^{10} +30x^8 +25x^6 \end{align}

NOTE: In the last line, we have moved the terms around so that the highest order term, \displaystyle 9x^{10} , comes first, followed by terms of decreasing order.