Question on completing the square obtaining the form $a(x+p)^2+q$

Question

From the last term in completing the square from the quadratic $ax^2+bx+c$, I was just wondering how $$-\left(\frac{b}{2a}\right)^2+c = \left(c-\frac{b^2}{4a}\right)$$ I would have gotten $$-\left(\frac{b}{2a}\right)^2+c=\left(c-\frac{b^2}{(2a)^2}\right)=\left(c-\frac{b^2}{4a^2}\right)$$ Books final answer was the following when completing the square $$ax^2+bx+c=a\left(x+\frac{b}{2a}\right)^2+\left(c-\frac{b^2}{4a}\right)$$

Answer 1

You forgot to multiply the $\left(\frac{b}{2a}\right)^2$ by $a$.