I'm finding it difficult to do this problem, its part of the system of linear equations with three variables. Find a,b,c so that for every x ∈ R this is valid:
$$x^2=a(x+2)^2+b(x+2)+c$$
Any help is appreciated, even if its just a tip on what to look for
Hint : Look at the coefficients of the polynomial to the left (you can also write it as $1\cdot x^2+0\cdot x+0$) and expand the square on the right , what system of $a,b,c$ you should solve to make the same polynomial on both sides?
Hint 2 : if you expand the right side you get $ax^2+(4a+b)x+4a+2b+c$ so you should impose : $ \begin{cases} a = 1\\ 4a+b=0 \\ 4a+2b+c=0\end{cases} $
to make the two sides equal.