# Help me with the multiplication of polynomials

Could you help me with this polynomial multiplication exercise?

• No bounty ?

You have to use the distributive rule :
(a+b+...) (c+d) =   a . (c + d)  +  b . (c + d) + ...
=   (a c + a d )  + ( b c + b d ) + ...
(where . as well as simple spaces as in a c, b c, ... denote multiplication.)

For example, the first  a . c  =  ( 3/2  x^5 ) . ( 2  x^3 ) =  3/2 . 2 . x^5 . x^3  = 3 x^8 .

The 0 terms can of course be omitted.
You can also first "factor out" x^2 from the second (...) and compute everything without that x² and in the end multiply everything with this x² , i.e., increase all powers by 2.

You can check your result by pasting the original expression into a symbolic online calculater, e.g. PARI/gp, see here : http://pari.math.u-bordeaux.fr/gp.html . You'll have to insert * for multiplication and ^ for powers, so you'll enter:

(3/2*x^5 + ...) * (2*x^3 + ...)

It will give you the expanded expression.
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