# Help me with the multiplication of polynomials

## 1 Answer

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:

It will give you the expanded expression.

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