\(a,f\left(x\right)+g\left(x\right)\\ =10x^5-5x^5-8x^4+2x^4+6x^3-4x^3-4x^2+6x^2+2x-8x+1+10+3x^6+2x^6\\ =5x^6+5x^5-6x^4+2x^3+2x^2-6x+11\\ f\left(x\right)-g\left(x\right)\\ =3x^6-2x^6+10x^5+5x^5-8x^4-2x^4+6x^3+4x^3-4x^2-6x^2+2x+8x+1-10\\ =x^6+15x^5-10x^4+10x^3-10x^2+10x-9\)
\(b,f\left(x\right) +g \left(x\right)=3x^4+2x^4+15x^3-15x^3+7x^2-7x^2+3x-3x-\dfrac{1}{2}+\dfrac{1}{2}=5x^4\\ f\left(x\right)-g\left(x\right)=3x^4-2x^4+15x^3+15x^3+7x^2+7x^2+3x+3x-\dfrac{1}{2}-\dfrac{1}{2}\\ =x^4+30x^3+14x^2+6x-1\)