[tex]\begin{gathered} (4x-3)(5x^2+6x-9)-2x(-\frac{x^2}{2}+\frac{11}{2}x+6) \\ 2x(-\frac{x^2}{2}+\frac{11}{2}x+6)=-x^3+11x^2+12x \\ (4x-3)(5x^2+6x-9)=20x^3+24x^2-36x-15x^2-18x+27 \\ (4x-3)(5x^2+6x-9)=20x^3+9x^2-54x+27 \\ 20x^3+9x^2-54x+27-(-x^3+11x^2+12x) \\ 20x^3+9x^2-54x+27+x^3-11x^2-12x \\ (20x^3+x^3)+(9x^2-11x^2)+(-54x-12x)+27 \\ 21x^3-2x^2-66x+27 \\ (4x-3)(5x^2+6x-9)-2x(-\frac{x^2}{2}+\frac{11}{2}x+6)=21x^3-2x^2-66x+27 \\ \\ \text{The standard form is }21x^3-2x^2-66x+27 \end{gathered}[/tex]
