a, \(f\left(x\right)=x^3+\left(-2x^2-x^2\right)+x-5\)
\(\Rightarrow f\left(x\right)=x^3-3x^2+x-5\)
\(g\left(x\right)=-x^3+3x^2+3x+\left(4-9\right)\)
\(\Rightarrow g\left(x\right)=-x^3+3x^2+3x-5\)
b,\(f\left(x\right)+g\left(x\right):\)
\(\Leftrightarrow f\left(x\right)+g\left(x\right)=x^3-2x^2+x-x^2-5+\left(-x^3+4+3x^2+3x-9\right)\)
\(\Leftrightarrow f\left(x\right)+g\left(x\right)=x^3-2x^2+x-x^2-5-x^3+4+3x^2+3x-9\)
\(\Leftrightarrow f\left(x\right)+g\left(x\right)=\left(x^3-x^3\right)+\left(-2x^2-x^2+3x^2\right)+\left(x+3x\right)+\left(-10\right)\)
\(f\left(x\right)-g\left(x\right):\)
\(\Leftrightarrow f\left(x\right)-g\left(x\right)=x^3-2x^2+x-x^2-5-\left(-x^3+4+3x^2+3x-9\right)\)
\(\Leftrightarrow f\left(x\right)-g\left(x\right)=x^3-2x^2+x-x^2-5+x^3-4-3x^2-3x+9\)
\(\Leftrightarrow f\left(x\right)-g\left(x\right)=\left(x^3+x^3\right)+\left(-2x^2-x^2-3x^2\right)+\left(x-3x\right)+\left(9-4-5\right)\)
\(\Leftrightarrow f\left(x\right)-g\left(x\right)=2x^3-6x^2-2x\)
\(a)f\left(x\right)=x^3-2x^2+x-x^2-5\)
\(f\left(x\right)=x^3+\left(-2x^2-x^2\right)+x-5\)
\(f\left(x\right)=x^3-3x^2+x-5\)
\(g\left(x\right)=-x^3+4+3x^2+3x-9\)
\(g\left(x\right)=-x^3+3x^2+3x+\left(4-9\right)\)
\(g\left(x\right)=-x^3+3x^2+3x-5\)
\(\text{b)f(x)+g(x)}=\left(x^3-3x^2+x-5\right)+\left(-x^3+3x^2+3x-5\right)\)
\(f\left(x\right)+g\left(x\right)=x^3-3x^2+x-5+-x^3+3x^2+3x-5\)
\(f\left(x\right)+g\left(x\right)=\left(x^3-x^3\right)+\left(-3x^2+3x^3\right)+\left(x+3x\right)+\left(-5-5\right)\)
\(f\left(x\right)+g\left(x\right)=4x-10\)
\(f\left(x\right)-g\left(x\right)=\left(x^3-3x^2+x-5\right)-\left(-x^3+3x^2+3x-5\right)\)
\(f\left(x\right)-g\left(x\right)=x^3-3x^2+x-5+x^3-3x^2-3x+5\)
\(f\left(x\right)-g\left(x\right)=\left(x^3+x^3\right)+\left(-3x^2-3x^2\right)+\left(x-3x\right)+\left(-5+5\right)\)
\(f\left(x\right)-g\left(x\right)=2x^2-6x^2-2x\)
