Building a dynamic query of a many-to-many relationship in Laravel 5

I am pretty new to the Laravel Eloquent ORM and am having difficulty building a dynamic query to query products of a category.

I parse the request object and return products according to what vars have been passed through. This is easy enough when I am querying a single Model but I want to know how to build a query dynamically if a category is passed through to. This is easy enough using standard MYSQL and PHP but I am unsure as to how this is achieved in LAravel.

Here is my code:

Product Model:

<?php

namespace App;

use Illuminate\Database\Eloquent\Model;

class Product extends Model
{
    protected $primaryKey = 'id',
              $table      = 'products',
              $fillable   = array('title', 'SKU', 'description', 'created_at', 'updated_at');

    public $timestamps = true;

    /**
     * Get the categories assoicated with the product
     *
     * @return \Illuminate\Database\Eloquent\Relations\BelongsToMany
     *
     */
    public function categories() {
        return $this->belongsToMany('App\Category')->withTimestamps();
    }
}

Category model:

<?php

namespace App;

use Illuminate\Database\Eloquent\Model;

class Category extends Model
{
    /**
     * Returns all products related to a category
     *
     * @return \Illuminate\Database\Eloquent\Relations\BelongsToMany
     */
    public function products() {
        return $this->belongsToMany('App\Product')->withTimestamps();
    }

}

Inside my product controller I have this function to get products which calls a method 'filterProduct' in a class called 'filtervars':

public function index(Request $request)
{
    return FilterVars::filterProduct($request->all());
}

And here is the filterProduct method:

public static function filterProduct($vars) {

        $query = Product::query();

        if((array_key_exists('order_by', $vars)) && (array_key_exists('order', $vars))) {
            $query = $query->orderBy($vars['order_by'], $vars['order']);
        }

        if(array_key_exists('cat', $vars)) {
            $query = $query->whereHas('categories', function($q) use ($vars){
                return $q->where('category_id', $vars['cat']);
            });
        }     

        return $query->get();

The product database migration:

class CreateProductsTable extends Migration
{
    /**
     * Run the migrations.
     *
     * @return void
     */
    public function up()
    {
        Schema::create('products', function(Blueprint $table) {
            $table->increments('id');
            $table->string('title', 75);
            $table->string('SKU')->unique();
            $table->text('description')->nullable();
            $table->timestamps();
        });
    }

And the migration which shows the structure of the categories table, the pivot table and foreign keys etc:

class CreateCategoriesTable extends Migration
{
    /**
     * Run the migrations.
     *
     * @return void
     */
    public function up()
    {
        Schema::create('categories', function (Blueprint $table) {
            $table->increments('id');
            $table->string('name');
            $table->string('description');
            $table->timestamps();
        });

        Schema::create('category_product', function(Blueprint $table) {
            $table->integer('product_id')->unsigned()->index();
            $table->foreign('product_id')->references('id')->on('products')->onDelete('cascade');

            $table->integer('category_id')->unsigned()->index();
            $table->foreign('category_id')->references('id')->on('categories')->onDelete('cascade');
            $table->timestamps();
        });
    }

I had a go at trying to incorporate the 'has' method on the query but this doesn't seem to work. can anyone advise as to where I am going wrong?

Thanks!