Question

Answer please.
Evaluate each of the following, using identity:
i) 102 × 98
ii) (1009) ²
iii) 161 x 161 – 61 x 61

Answer 1

Evaluate each of the following, using identity:

(i) 102 × 98

(ii) (1009)²

(iii) 161 x 161 – 61 x 61

Solution :

i) 102 × 98

Here we will use the identity :

• [(a + b)(a – b) = a² – b²]

102 × 98 = (100 + 2)(100 – 2)

⠀⠀⠀⠀⠀ = (100)² – 2²

⠀⠀⠀⠀⠀ = 10000 – 4

⠀⠀⠀⠀⠀ = 9996

ii) (1009)²

Here we will use the identity :

• (a + b)² = a² + 2ab + b²

(1009)² = (1000 + 9)²

⠀⠀⠀⠀ = (1000)² + 2(1000)9 + 9²

⠀⠀⠀⠀ = 100000 + 2 × 9000 + 81

⠀⠀⠀⠀ = 100000 + 18000 + 81

⠀⠀⠀⠀ = 1018081

iii) 161 x 161 – 61 x 61

Here we will use the identity :

• [(a + b)(a – b) = a² – b²]

161 x 161 – 61 x 61 = (161 + 61)(161 – 61)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= (161)² – (61)²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 25921 – 3721

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 22200