如何修复Laravel项目中具有多对多关系的未定义变量产品？

Question

我试图使用Laravel中的多对多关系列出数据库中与特定用户连接的所有产品，但出现此错误：

Undefined variable: products (View: C:\xampp\htdocs\admin\resources\views\welcome.blade.php)

这是我的代码：

Product.php

<?php
namespace App;

use App\User;
use Illuminate\Database\Eloquent\Model;

class Product extends Model
{
    protected $fillable = ['file'];

    public function users()
    {
        return $this->belongsToMany(User::class, 'product_user', 'product_id', 'user_id');
    }
}

User.php

<?php

namespace App;

use App\Product;
use Illuminate\Contracts\Auth\MustVerifyEmail;
use Illuminate\Foundation\Auth\User as Authenticatable;
use Illuminate\Notifications\Notifiable;

class User extends Authenticatable
{
    use Notifiable;

    protected $fillable = [
    'name', 'email', 'password',
    ];

    protected $hidden = [
    'password', 'remember_token',
    ];

    protected $casts = [
    'email_verified_at' => 'datetime',
    ];

    public function products()
    {
        return $this->belongsToMany(Product::class, 'product_user', 'user_id', 'product_id');
    }
}

ProductController.php

<?php

namespace App\Http\Controllers;

use App\Product;
use Illuminate\Http\Request;

class ProductController extends Controller
{

    public function index()
    {
        $products = Product::with('users')->get();
        return view('welcome', compact('products'));
    }
}

welcome.blade.php

@if($products)
    <table class="table">
        <thead>
            <th>#</th>
            <th>Product Name</th>
            <th>Created At</th>
        </thead>
        <tbody>
        @foreach ($products as $product)
            <tr>
                <td>{{ $product->id }}</td>
                <td>{{ $product->file }}</td>
                <td>{{ date('M j, Y', strtotime($product->created_at)) }}</td>
                   <td>
                   @foreach ($product->users as $user)
                       <td>{{ $user->name }}</td>
                   @endforeach
                 </td>
            </tr>
         @endforeach
         </tbody>
      </table>
 @endif

我在网上四处寻找类似的问题，但是我陷于困境，似乎找不到问题，因此，如果有人可以提供一些见解，将不胜感激。