# 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

Why does this work?

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

= 100a(a + 1) + bc. |

Another example: compute 242×248, with

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

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

Now appending 16 (= 2×8) we get

|Contact| |Front page| |Contents| |Algebra| |Rapid math| |Store|

Copyright © 1996-2017 Alexander Bogomolny

62028617 |