Product of 10a + b and 10a + c where b + c = 10

This is quite similar to the squaring of numbers that end with 5.

For example, compute 113×117, where a = 11, b = 3, and c = 7. First compute 11·(11 + 1) = 11·12 = 132 (since 3 = 1 + 2). Next, append 21 (= 3×7) to the right of 132 to get 13221!

Why does this work?

 (10a + b)(10a + c)= 100a² + 10a·(b + c) + bc
  = 100a(a + 1) + bc.

Another example: compute 242×248, with a = 24, b = 2, and c = 8. Then

24·(24 + 1) = 24² + 24 = 576 + 24 = 600.

(Also 24×25 = 25² - 25 = 625 - 25 = 600.)

Now appending 16 (= 2×8) we get 242×248 = 60016.


Related material
Read more...

  • Multiplication by 9, 99, 999, (Multiply + Subtract) etc.
  • Squaring 2-Digit Numbers
  • Division by 5
  • Multiplication by 2
  • Multiplication by 5
  • Multiplication by 9, 99, 999, etc. (Something Special)
  • Product of 10a + b and 10a + c where b + c = 10
  • Product of numbers close to 100
  • Product of two one-digit numbers greater than 5
  • Product of 2-digit numbers
  • Squaring Numbers in Range 26-50
  • Squaring Numbers in Range 51-100
  • Squares of Numbers That End in 5
  • Squares Can Be Computed Squentially
  • How to Compute Fast Any Square
  • Adding a Long List of Numbers
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