Why Constant Returns to Scale Suggests Certain Relation I'm self studying intermediate macroeconomics by reading a textbook and I came across a relationship that I'm not quite sure how it is derived. 

Let $F(K,L)$ be a production function where $K$ is capital stock and $L$ is the labor force. Assuming constant returns to scale, I'm not sure how to derive $$F(K,L) = F_K(K,L)K + F_L(K,L)L,$$ where $F_x$ denotes the partial derivative of $F$ with respect to $x$.
The result follows from Euler's Theorem on homogenous equations. This theorem states that if a function $f(x,y)$ is homogeneous of degree $\lambda$ then the following holds:

$\lambda f(x,y)= x \frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y}$

A (production) function with constant returns to scale is homogeneous of degree 1 by definition. The definition of constant returns to scale is basically the same as the definition of homogeneity of degree 1. That means $\lambda=1$, which proves the result you need.