is it impassible to write style in another xaml file and attribute the object in another xaml page?

Do you mean you want to put your xaml styles in one file and use them in another? yes.

you can do that. You can create a ResourceDictionary to hold your styles and be used by many other files. you just need to include it as a resource in each file or you can add it to the Application.Resources in your app.xaml then it will be available to the entire application.

<Application x:Class="myNameSpace.App"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
    <Application.Resources>
        <ResourceDictionary>
            <ResourceDictionary.MergedDictionaries>
                <ResourceDictionary Source="pack://application:,,,/SomeDllWithResource;component/Layout/WPFDataGridLayout.xaml" />
                <ResourceDictionary  Source="myResources.xaml"></ResourceDictionary>
            </ResourceDictionary.MergedDictionaries>
        </ResourceDictionary>
    </Application.Resources>
</Application>

once you've created the Resource dictionary you can include it like above for 'myResources.xaml' that line can be put in the resources section of a specific file or in the app.xaml like the example above.