[latex]( x^{2} +x+1)(2 x^{2} -x+2)= \ =x^{2} *2 x^{2} - x^{2} *x+ x^{2} *2+x*2 x^{2} -x*x+x*2+2 x^{2} -x+2= \ = 2x^{4}- x^{3}+2 x^{2} +2 x^{3} - x^{2} +2x+2 x^{2} -x+2= \ =2 x^{4}- x^{3}+2 x^{3}+2 x^{2} - x^{2} +2 x^{2} +2x-x+2= \ =2 x^{4}+ x^{3}+3 x^{2} -x+2 \ (3x-2y+4)(5x+2y-3)= \ =3x*5x+3x*2y-3x*3-2y*5x-2y*2y+2y*3+ \ +4*5x+4*2y-4*3= \ =15 x^{2} +6xy-9x-10xy-4 y^{2} +6y+20x+8y-12= \ =15 x^{2} -4 y^{2} +11x+14-4xy-12 \ [/latex] [latex](3 a^{3} +2 a^{2} +a)(-5 a^{2} +6a+8)= \ =-15 a^{5} +18 a^{4} +24 a^{3}-10 a^{4} +12 a^{3}+16 a^{2}-5 a^{3} +6 a^{2} +8a \ (3km+4k-2m)(3km-4k+2m)= \ =9 k^{2} m^{2} -12 k^{2} m+6k m^{2} +12 k^{2}m-16 k^{2} +8km-6km^{2}+ \ +8km-4m^{2}= \ =9k^{2}m^{2}-16k^{2}-4m{2}+16km[/latex] .
