Question

Use formulas to find the values of the following:

(i) 62²
(ii) 28²
(iii) 202²
(iv) 38 × 42

Answer 1

(i) 62²
62 = 60 + 2
∴ 62² = (60 + 2)²
Thus, we can use the identity (a + b)² = a² + 2ab + b² .
∴ 62² = (60 + 2)²
= (60)² + 2 (60) (2) + (2)²
= 3600 + 240 + 4
= 3844

(ii) 28²
28 = 30 − 2
∴ 28² = (30 − 2)²
Thus, we can use the identity (a − b)² = a² − 2ab + b² .
∴ 28² = (30 − 2)²
= (30)² − 2 (30) (2) + (2)²
= 900 − 120 + 4
= 900 + 4 − 120
= 904 − 120
= 784

(iii) 202²
20² = 200 + 2
∴ 202² = (200 + 2)²
Thus, we can use the identity (a + b)² = a² + 2ab + b² .
∴ 202² = (200 + 2)²
= (200)² + 2 (200) (2) + (2)²
= 40000 + 800 + 4
= 40804

(iv) 38 × 42
38 = 40 − 2
42 = 40 + 2
∴ 38 × 42 = (40 − 2) (40 + 2)
The expression (40 − 2) (40 + 2) is of the form (a + b) (a − b).
Thus, we can use the identity (a + b) (a − b) = a² − b² .
∴ 38 × 42 = (40 − 2) (40 + 2)
= (40)² − (2)²
= 1600 − 4
= 1596