Multiplication of two Taylor expansions I'm trying to calculate a Taylor expansion which is :  $\cos(x). exp(x)$  in the neighborhood of 0 in order 3
this is the result I got : 
$$\cos(x). exp(x) = \left(1-\frac{x²}{2}+\epsilon(x)x^3\right) . \left(1+x+\frac{x²}{2}+\frac{x^3}{6}+\epsilon(x)x^3\right)$$
And now I need to multiply the two expressions.
I think that there is a method where we use a table to multiply to Taylor expansion, but I don't know hw to do it.

You use the distributive property, so the expansion starts off $1\cdot 1  +1\cdot x +1 \cdot \frac {x^2}2 -\frac {x^2}2\cdot 1$, then collect the terms of the same degree
