Dear Sir,
I am writing to apologize for the bad performance of the washing machine you bought from our department store. I do hope(希望的语气可以稍微强烈一点) you can accept my sincere apologies.
In fact, the mistake is due to our ignorance(万能开头，啥错误不是失误呀). The manufacturer of the washing machine has cooperated(完成时要注意。) with us for ten years, and never made(过去没有犯过错误，现在有了) a mistake like this, then we did not double check the product.(自己还是有责任的) I want you to know that your trust is very important to us, so we will send(解决方案是将来时) an employee to take the machine back and give you a full refund.
Once again, I am sorry for any inconvenience caused by it, and hope you can accept the apologies.(再次道歉)