[latex]a)\(-8-5x^5+12x^7)+(frac{1}{2}-2x^7-4x^5-frac{3}{4}x^3)=\ \=-8-5x^5+12x^7+frac{1}{2}-2x^7-4x^5-frac{3}{4}x^3 =\ \=10x^7-9x^5 -frac{3}{4}x^3-7frac{1}{2}[/latex] [latex]b)\ \(frac{5}{7}x-7x^4)-(frac{3}{4}x^3-frac{4}{7}x+3-7x^4)=\ \=frac{5}{7}x-7x^4-frac{3}{4}x^3+frac{4}{7}x-3+7x^4=\ \=-frac{3}{4}x^3+frac{9}{7}x -3[/latex] [latex]c)\-2x(3-4x^4-7x^5)+x^5(5x-8)=\ \-6x+8x^5+14x^6+5x^6-8x^5=19x^6-6x[/latex] [latex]d)\ \(5x^4+2)(x^2-1)-4x^3(3x^3-x)=\ \=5x^6-5x^4+2x^2-2-12x^6+4x^4=\ \=-7x^6-x^4+2x^2-2[/latex]
[latex]a) \ (-8+5 x^{5} +12 x^{7} )+( frac{1}{2} -2 x^{7} -4 x^{5} - frac{3}{4} x^{3} )= \ =-8-5 x^{5} +12 x^{7} + frac{1}{2} -2 x^{7} -4 x^{5} - frac{3}{4} x^{3} = \ =10 x^{7} -9 x^{5} - frac{3}{4} x^{3} -7 frac{1}{2} [/latex] [latex]b) \ ( frac{5}{7} x-7 x^{4} )-( frac{3}{4} x^{3} - frac{4}{7} x+3-7 x^{4} )= \ = frac{5}{7} x-7 x^{4} - frac{3}{4} x^{3} + frac{4}{7} x-3+7 x^{4} = \ =- frac{3}{4} x^{3} +1 frac{2}{7} -3[/latex] [latex]c) \ -2x(3-4 x^{4}-7 x^{5} )+ x^{5} (5x-8)= \ =-6x+8 x^{5} +14 x^{6} +5 x^{6} -8 x^{5} = \ =19 x^{6}-6x[/latex] [latex]d) \ (5 x^{4} +2)( x^{2} -1)-4 x^{3} (3 x^{3} -x)= \ =5 x^{6} -5 x^{4} +2 x^{2} -2-12 x^{6} +4 x^{4} = \ =7 x^{6} - x^{4} +2 x^{2} -2[/latex]
