This examples shows how to remove white spaces from the string

 public function removeSpaces(str:String):String {
 if (str == null) { return ''; }
 return str.replace(/\s+/g, '');
 }

This is the complete flex example

<?xml version="1.0" encoding="utf-8"?>
<mx:Application
 xmlns:mx="http://www.adobe.com/2006/mxml"
 layout="absolute">
 <mx:Script>
 <![CDATA[

 public function removeSpaces(str:String):String {
 if (str == null) { return ''; }
 return str.replace(/\s+/g, '');
 }
 public function on_trim_button():void {
 reultText.text = removeSpaces(originalText.text);
 }
 ]]>
 </mx:Script>
 <mx:Button x="74" y="101" label="Trim Spaces" click="on_trim_button()"/>
 <mx:TextArea x="74" y="42" id="originalText" />
 <mx:TextArea x="74" y="157" id="reultText" />
 <mx:Label x="74" y="16" text="Enter Text" width="160"/>
 <mx:Label x="74" y="131" text="Enter Text" width="160"/>
</mx:Application>