Product of numbers that only differ in units. Multiplying by 11. To multiply a 2-digit number by 11, take the sum of its digits. If it's a single digit number, just write it between the two digits. If the sum is 10 or more, do not forget to carry 1 over.
Subtraction is often faster in two steps instead of one.
Addition is often faster in two steps instead of one. It's often faster to add a digit at a time starting with higher digits. Multipliply, then subtract. When multiplying by 9, multiply by 10 instead, and then subtract the other number. The same applies to other numbers near those for which multiplication is simplified.