Question

Take a square of nine numbers in the calendar and make the 4 numbers in the 4 corners.

Multiply the angle to angle number pairs. Find the difference of the products.

3 × 19 = 57

17 × 5 = 85

85 – 57 = 28

(i) Take a square of nine numbers and follow the same method as above.

(ii) Explain the reason why we get the difference in the squares as 28 on the basis of algebra.

Answer 1

(i)

18 × 6 – 4 × 20 

108 – 80 = 28

(ii)

(x + 6) (x – 6) – (x – 8) (x + 8)

(x² – 6²) – (x² + 8²)

= x² – 6² – x² – 8²

= 8² – 6²

= (8 + 6) (8 – 6)

= 14 × 2 = 28