Suppose that a(x+b(x+3))=2(x+6) for all real values of x, find a+b. I have tried subsituting y for x+3 and solving that way but I could not find a solution. Could someone point me in the right direction? Thanks!

Guest Sep 25, 2022

#2**+1 **

Simplify:

\(a(x+b(x+3)) = 2(x+6)\)

\(a(x+bx+3b) = 2x + 12\)

\(ax+abx+3ab = 2x + 12\)

Equate coefficicents:

\(ab = 4\)

\(a + ab = 2\)

Solving this system, we find \(a = -2\) and \(b = -2\) so \(a + b = \color{brown}\boxed{-4}\)

BuilderBoi Sep 25, 2022