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Aus Online Mathematik Brückenkurs 1

When the expression 1+x+x2+x32−x+x2+x4  is expanded out,

every term in the first bracket is multiplied by every term in the second bracket, i.e.

1+x+x2+x32−x+x2+x4=12+1−x+1x2+1x4+x2+x−x+xx2+xx4+x22+x2−x+x2x2+x2x4+x32+x3−x+x3x2+x3x4

If we only want to know the coefficient in front of x, we do not need to carry out the complete expansion of the expression; it is sufficient to find those combinations of a term from the first bracket and a term from the second bracket which, when multiplied, give an x1 -term. In this case, we have two such pairs: 1 multiplied by - x and x multiplied by 2 ,

1+x+x2+x32−x+x2+x4=+1−x+x2+ 

so that the coefficient in front of x is −1+2=1

We obtain the coefficient in front of x2 by finding those combinations of a term from each bracket which give an x2 -term; these are

1+x+x2+x32−x+x2+x4=+1x2+x−x+x22+ 

The coefficient in front of x2 is 1−1+2 .