a,f(x)+g(x)=\(\left(a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0\right)+\left(b_nx^{n-1}+...+b_1x+b_0\right)\)
=\(a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0+b_nx^n+b_{n-1}x^{n-1+...+b_1x+b_0}\)
\(=\left(a_nx^n+b_nx^n\right)+\left(a_{n-1}x^{n-1}+b_{n-1}x^{n-1}\right)+...+\left(a_1x+b_1x\right)+\left(a_0+b_0\right)\)
b
f(x)+g(x)=\(\left(a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0\right)+\left(b_nx^n+b_{n-1}x^{n-1}+...+b_1x+b_0\right)\)
\(=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0-b_nx^n-b_{n-1}-b_1x+b_0\)
\(=(a_nx^n-b_nx^n)+(a_{n-1}x^{n-1}-b_{n-1}x^{n-1})+...+(a_1x-b_1x)+\left(a_0+b_0\right)\)
\(=\left(a_n-b_n\right)x^n+(a_{n-1}-b_{n-1})x^{n-1}+...+\left(a_1-b_1\right)x+\left(a_0-b_0\right)\)
