I need help in understanding how the summation of the product of two polynomials is written.

$(a\_{0} +a\_{1}x +a\_{2}x^{2})(b\_{0} +b\_{1}x + b\_{2}x^{2}) =\\ (a\_{0}b\_{0})x^{0} + (a\_{1}b\_{0} + b\_{1}a\_{0})x + (a\_{2}b\_{0} +a\_{1}b\_{1} + a\_{0}b\_{2})x^{2} + (a\_{1}b\_{2} + a\_{2}b\_{1})x^{3} + (a\_{2}b\_{2})x^{4}$

I can not figure out how to write this as a general summation.
Thanks