When you have a laravel project with a form and you would like to make jquery ajax form submit and validation, you can use below codes,

ajax_form_validation.js

$(function(){
   $('.form-horizontal').on('click', function(e){
        e.preventDefault();
         var $form = $('.form-horizontal');
         var url = $form.attr('action');
         var method = $form.attr('method');
        $.ajax({
            url: url,
            type: method,
            data: $form.serialize(),
            success: function(data){
                alert("Successfully submitted.")
            },
            error: function (response) {
                var errors = JSON.parse(response.responseText);
                 //handle failed validation
                associate_errors(errors, $form);
              }
        });
   }); 

   function associate_errors(errors, $form)
    {
        //remove existing error classes and error messages from form groups
        $form.find('.form-group').removeClass('has-errors').find('.help-text').text('');
         $.each( errors, function( key, value) {
            console.log(value);
            // errorString += '<li>' + value + '</li>';
            // find each form group, which is given a unique id based on the form field's name
            var $group = $form.find('#' + key);
            //add the error class and set the error text
            $group.addClass('has-errors').text(value);
        });
    }
});