How to solve 497*505 using suitable identities

Step-by-step explanation:

497 = 500 - 3

505 = 500 + 5

(x + a) (x + b) = x² + (a + b) x + ab

x = 500; a = - 3; b = + 5

(500 - 3) (500 + 5) = (500) ² + (-3 + 5) 500 + (-3) * 5

= 250000 + (2) * 500 + (-15)

=250000 + 1000 - 15

= 250985