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
On
Let $C_m$, coefficients be $$sum a_j*b_k$$ where j+k = m
So the resulting polynomial is
Sum m=0 to 4 of $C_m$ * $x^m$
Please fix my MathJax/ LaTeX, simply figuring out the answer and how to notate it took significant effort. I invite you or encourage you to check this by writing out a few terms of the sum.
Hint
Distribute the product $$(a_{0} +a_{1}x +a_{2}x^{2})(b_{0} +b_{1}x + b_{2}x^{2}) =$$ $$(a_{0} +a_{1}x +a_{2}x^{2}) b_0 +(a_{0} +a_{1}x +a_{2}x^{2}) b_{1}x+(a_{0} +a_{1}x +a_{2}x^{2}) b_{2}x^{2}$$ Expand now what is inside the brackets and group together the terms showing the same power of $x$. Remember that $x^0=1$