Question

999*999, Evaluate the given product without actual multiplication.

Answer 1

Interesting question here,

Although if you want to multiply any numbers without actually doing any multiplication you can refer to the japanese method of multiplication, the link of which i have mentioned in the comment section

But i would also like to recommend one of these methods where you can multiply large numbers mentally

Here is the method,

Try expressing the numbers in form of numbers which are divisible by 10

Example:

9 can be expressed as 10-1

And then you can do the multiplication,

Now, let us take the sum you have mentioned above,

(1000- 1)×(1000-1)

1000000 - 2000 + 1

998001

This is how simplified multiplication can be performed

Hope this helps!!!!!!!!!!!!!

Answer 2

Solution :

999 × 999

= ( 999 )²

= ( 1000 - 1 )²

*******************************************
we know the algebraic identity ,

( a - b )² = a² - 2ab + b²

********************************************

= ( 1000 )² - 2 × 1000 × 1 + 1²

= 1000000 - 2000 + 1

= 998001

Therefore ,

999 × 999 = 998001

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