Too much white space when using the align-environment

You could use the alignat environment, which is similar to align.

\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
\usepackage{mathtools}
\usepackage{amssymb}

\begin{document}
  \begin{alignat}{2}
    \prod a+bm      &\quad \text{is a square in} &&\quad\mathbb{R}\\
    \prod a+b\theta &\quad \text{is a square in} &&\quad\mathbb{R}[\theta]
  \end{alignat}
\end{document}

In the »Math mode« document you can find more about advanced math typesetting.

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Update:

As requested the same example but with all columns left aligned.

\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
\usepackage{mathtools}
\usepackage{amssymb}

\begin{document}
  \begin{alignat}{3}
    &\prod a+bm      &&\quad \text{is a square in} &&\quad\mathbb{R}\\
    &\prod a+b\theta &&\quad \text{is a square in} &&\quad\mathbb{R}[\theta]
  \end{alignat}
\end{document}

---

\documentclass{article}
\usepackage{amsmath, amssymb}
\begin{document}
\begin{align}                                                                      
  \prod a+bm &\phantom{=} \text{is a square in}\quad \mathbb{R}\\                  
  \prod a+b\theta &\phantom{=} \text{is a square in}\quad \mathbb{R}[\theta]       
\end{align}
\end{document}

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Flush left as requested:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\makeatletter
\newenvironment{lflalign}{%                                                         
  \def\align@preamble{%                                                             
    &\strut@                                                                        
    \setboxz@h{\@lign$\m@th\displaystyle{####}$}%                                   
    \ifmeasuring@\savefieldlength@\fi                                               
    \set@field                                                                      
    \hfil                                                                           
    \tabskip\z@skip                                                                 
    &\setboxz@h{\@lign$\m@th\displaystyle{{}####}$}%                                
    \ifmeasuring@\savefieldlength@\fi                                               
    \set@field                                                                      
    \hfil                                                                           
    \tabskip\alignsep@                                                              
  }                                                                                 
  \flalign}
{\endflalign}
\makeatother
\begin{document}
\begin{align}                                                                       
  \prod a+bm & \phantom{=}\text{is a square in}\quad \mathbb{R}\\                   
  \prod a+b\theta & \phantom{=}\text{is a square in}\quad \mathbb{R}[\theta]        
\end{align}
\begin{lflalign}
  \prod a+bm & \phantom{=}\text{is a square in}\quad \mathbb{R}\\
  \prod a+b\theta & \phantom{=}\text{is a square in}\quad \mathbb{R}[\theta]
\end{lflalign}
\end{document}