How can I solve 21x29 in 5 seconds?

21\,\times\,29=(25-4)\times(25+4)=25^2-4^2=625-16=609

Recognize that (a-b)(a+b)=a^2-b^2 and that this fits the pattern. Make sure you've memorized all of the squares up to (at least) 25 and can subtract (or add) quickly in your head.

Another way to approach this one easily in your head is to recognize that

21 x 29 = (20 x 29) + (1 x 29)

20 x 29 is simply 2 x 29 (which equals 58, of course) with an extra zero at the end (i.e. 20 x 29 = 580)

Then it's just a matter of adding the two numbers.

(20 x 29) + (1 x 29) = 580 + 29 = 609

Another way to approach this one easily in your head is to recognize that

21 x 29 = (20 x 29) + (1 x 29)

20 x 29 is simply 2 x 29 (which equals 58, of course) with an extra zero at the end (i.e. 20 x 29 = 580)

Then it's just a matter of adding the two numbers.

(20 x 29) + (1 x 29) = 580 + 29 = 609

I like this answer... that's the way I'd do it... its easier... :)

Try this approach:

2 1
| |
2 9
--------
4 20 9

=6 0 9

Step 1: Multiply 1 and 9 =9
Step 2: Multiply 2 and 2 =4
Step 3: Cross multiply 2 and 9 = 18
Step 4: Cross multiply 1 and 2 = 2
Step 5: Add the answers from step 3 and 4 = 20
We get number 20 in the step 5, so the 2 is carried over to the left
and added to 4 which gives 609.

BPNAIR

21(30-1)
630-21
609