Lösung 2.1:4b
Aus Online Mathematik Brückenkurs 1
When the expression
is expanded out, every term in the first bracket is multiplied by every term in the second bracket, i.e.
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 x-term. In this case, we have two such pairs: 1 multiplied by -x and x multiplied by 2,
so that the coefficient in front of x is \displaystyle -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
The coefficient in front of x² is \displaystyle 1-1+2=2\,.
