Sign change during factorization polynomial

Question

While trying to brush up on some basic calculus, I can’t understand where the positive sign (1+) comes from in the denominator.

Answer 1

Look at the denominator, and recall that $--$ becomes $+$.

Then $$4x-(-4x)\sqrt{1-\frac{3}{16x}}=4x+4x\sqrt{1-\frac{3}{16x}}\\ =(4x)\cdot 1+(4x)\cdot\sqrt{1-\frac{3}{16x}}=(4x) \cdot \left(1+\sqrt{1-\frac{3}{16x}}\right)$$

Now make $4x$ a common factor.

Answer 2

The sign is in the denominator, not the numerator. Here we are using the distributive law. The $1$ comes from the $4x$ term and the $+$ comes from the two minus signs.