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Let’s use algebra. starting with x,y, the square of the difference is is = + - 2

the square of the sum is

= + + 2

what if we subtract the square of the difference from the square of the sum.

- = (+ + 2 - (+ - 2)

- =

writing this in reverse

= -

for example, 24= 4

= here x=6 and y=1

= -

= -

= 7² – 5²

similarly 24 can also be written as

24 = 432

= here x=3 and y=2

= -

= -

= 5² – 1²

so 24 =7² – 5²= 5² – 1²

other multiple of 8,

32 = 9² – 7² = 6² – 2²

32 = 481

= here x=8 and y=1

= -

= -

= 9² – 7²

similarly 32 can also be written as

32 = 442

= here x=4 and y=2

= -

= -

32 = 9² – 7² = 6² – 2²