Novice question

Question

How does this factorisation work? $$f(x) = 2^x + 1 + x\ 2^x\ln(2) = (x\ln(2)+1)\ 2^x+1 $$

Thank you.

Answer 1

Let $2^x=A$ and $x=B$ then

$$2^x + 1 + x\ 2^x\ln 2=$$

$$=A+1+BA\ln 2=A+BA\ln 2+1=(1+B\ln 2)A +1=$$

$$=(1+x\ln 2)2^x+1$$