TabLayout not filling width when tabMode set to 'scrollable'

Instead of creating custom TabLayout and hacking around or creating more layouts which acts as wrapper around TabLayout only for background. Try this,

<android.support.design.widget.TabLayout
    android:id="@+id/tabs"
    style="@style/MyColorAccentTabLayout"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    <!-- Instead of setting app:tabBackground -->
    android:background="@color/colorAccent"
    app:tabGravity="fill"
    app:tabMode="scrollable"/>

This will set background to behind tabLayout instead of setting background behind every tab.

androidx version:

<androidx.viewpager.widget.ViewPager
    android:id="@+id/view_pager"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    app:layout_behavior="@string/appbar_scrolling_view_behavior" >
    <com.google.android.material.tabs.TabLayout
        android:id="@+id/tabs"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        app:tabMaxWidth="0dp"
        app:tabGravity="fill"
        app:tabMode="fixed"
        />
</androidx.viewpager.widget.ViewPager>

***** BELOW IS OLD ANSWER *****

Try this one, it's a workaround which sets tabMaxWidth="0dp", tabGravity="fill" and tabMode="fixed".

 <android.support.v4.view.ViewPager
     android:id="@+id/container"
     android:layout_width="match_parent"
     android:layout_height="match_parent"
     app:layout_behavior="@string/appbar_scrolling_view_behavior">
     <android.support.design.widget.TabLayout
         android:id="@+id/tabs"
         android:layout_width="match_parent"
         android:layout_height="wrap_content"
         app:tabMaxWidth="0dp"
         app:tabGravity="fill"
         app:tabMode="fixed"/>
</android.support.v4.view.ViewPager>

Screenshot on a 10 inch tablet: