Compute the following in head:682 – 322

using identity - =682 – 322 = (68+32)(68-32)= (100) (36)= 3600

Q1 of 95 Page 83

Compute the following in head:
68² – 32²

using identity - =

68² – 32² = (68+32)(68-32)

= (100) (36)

= 3600

Some natural numbers can be written as a difference of two perfect squares in two ways. For example.

24 = 7² – 5² = 5² – 1²

32 = 9² – 7² = 6² – 2²

40 = 11² – 9² = 7² – 3²

In how many different ways can we write multiples of 16, starting with 48 as the difference of two perfect squares?

Compute the following in head:

68² – 32²

Compute the following in head:

Questions · 95

4. Identities

1 1 1 1 1 1 2 2 2 2 2 2 3 3 4 4 1 1 1 2 2 2 2 2 2 3 3 4 4 5 5 1 1 1 1 1 1 1 1 2 2 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 1 1 1 1