Binomial expansion up to $x^2$

Question

1. Use the binomial expansion to show that $ \sqrt{(4-x)} $ is $2- \frac14x + kx^2 $

2. Use the binomial expansion to show that $ \sqrt{\frac{1+4x}{1-x}} $ is $ 1 + \frac52x - \frac58x^2 $

No idea where to start. Help appreciated

Answer 1

In the comments, it became apparent that you were not aware that the binomial expansion $$(x+y)^n=x^n+nx^{n-1}y+\dfrac{n(n-1)}2x^{n-2}y^2+...$$ can be valid even when $n$ is not an integer, though in that case it becomes an infinite series.

That is where you should start. Let me know if you need further help.