Simple multiplication method for head

Question

Please tell me the simplest ways for multiplication of complex number in my head like 234 x 23 =......    and 3456 x 34567=....

Answer 1

see --

   http://www.speed-math.com/story.htm

 

and

 

The Trachtenberg Speed System of Basic Mathematics

Paperback – August 8, 2011
Jakow Trachtenberg (Author), Ann Cutler (Translator), Sam Sloan (Introduction)

Paperback: 272 pages
Publisher: Ishi Press (August 8, 2011)
Language: English
ISBN-10: 4871877094
ISBN-13: 978-4871877091

Answer 2

The two best ways are still (1) pencil & paper, and (2) use of calculator.

 

There is sometimes seen on TV a promo for a guy who teaches a bunch of ARITHMETIC tricks to young people, and claims "you can do MATH in your head".  Math is a lot more than speedy arithmetic, though.

 

One idea: 23(234) = 23(230) + 23(4) which is easy if you have memorized 23 squared; 23² = (20 + 3)²

can be done in one's head as 20² + 2•20•3 + 3² which is 400 +120 + 9, etc, etc.

 

In the time it's taken to explain this, you would have the answer already, by using either of the methods (1) or (2).