[tex]\displaystyle\bf\\(a-3)\cdot(a^{2} +4a+2)=\\\\\\=a\cdot a^{2} +a\cdot 4a+a\cdot 2-3\cdot a^{2} -3\cdot 4a-3\cdot 2=\\\\\\=a^{3} +4a^{2} +2a-3a^{2} -12a-6=\\\\\\=a^{3} +(4a^{2} -3a^{2} )+(2a-12a)-6=a^{3} +a^{2} -10a-6[/tex]