The video below explains the algorithm using the distributive property.
When multiplying by more than one digit, you just have to remember what you know about place value. When multiplying and number by a multiple of 10, your product will always end in a zero. Then same is true for multiplying by any multiple of 100, your product will always end in two zeros. Keep this in mind when using the traditional algorithm because when you multiply by a new place value you will add the appropriate number of zeros to your product in the problem. Here's an example, notice the bolded zero. That is placed there because your are multiplying in the tens place. If you had a third digit, you would add two zeros because your are multiplying by the hundreds place.
Here's another Khan Academy video for further explanation.