\[(3-x)^4(3+x)^4\]
notice that \[9-x^2=(3-x)(3+x)\]
so\[\begin{equation} \begin{aligned} (3-x)^4(3+x)^4 &= (9-x^2)^4 \\ &= {}^4C_4 9^4(-x^2)^0+ {}^4C_3 9^3(-x^2)^1+{}^4C_2 9^2(-x^2)^2 \\ &+ {}^4_1 9^1(-x^2)^3+{}^4C_0 9^0 (-x^2)^4 \\ &= 6561-2916x^2+486x^4-9x^6+x^8 \end{aligned} \end{equation}\]