FOIL Method for 2-Digit Multiplication

  1. Multiply the first digits (tens × tens)
  2. Add the outer and inner products (tens × ones + ones × tens)
  3. Multiply the last digits (ones × ones)
  4. Combine, carrying when needed

Example:

23 × 41
First: 2 × 4 = 8
Outer + Inner: (2×1) + (3×4) = 2 + 12 = 14
Last: 3 × 1 = 3

Add carry: 8 + 1 = 9  Middle: 4  Right: 3

23 × 41 = 943

Another example:

34 × 52
First: 3 × 5 = 15
Outer + Inner: (3×2) + (4×5) = 6 + 20 = 26
Last: 4 × 2 = 8

Add carry: 15 + 2 = 17  Middle: 6  Right: 8

34 × 52 = 1768

Challenge example:

45 × 67
First: 4 × 6 = 24
Outer + Inner: (4×7) + (5×6) = 28 + 30 = 58
Last: 5 × 7 = 35

Add carry: 24 + 5 = 29  Middle: 8  Right: 5

45 × 67 = 3015

This is perhaps the most versatile method, but use it only when you have to since it takes a bit more time.