Question

Use appropriate formulae and compute:(i) (103)²; (ii) (96)²; (iii) 107 × 93;(iv) 1008 × 992; (v) 185² − 115².

Answer 1

Answer:

(i)  10609

(ii) 9216

(iii) 9951

(iv) 999936

(v) 21000

Step-by-step explanation:

(i) Algebraic identify (a + b)²  = a²  + 2ab + b²

(103)² = (100 + 3)²

(103)² = 100²  + 2(100)(3) + 3²

(103)² = 10000  + 600 +  9

(103)² = 10609

(ii) Algebraic identify (a - b)²  = a²  - 2ab + b²

(96)² = (100 - 4)²

(96)² = (100)² - 2(100)(4) + 4²

(96)² = 10000 - 800 + 16

(96)² = 9216

(iii) Algebraic identify (a + b)(a - b)  = a² - b²

107 x 93 = (100 + 7)(100 - 7)

107 x 93 = 100² - 7²

107 x 93 = 10000 - 49

107 x 93 = 9951

(iv) Algebraic identify (a + b)(a - b)  = a² - b²

1008 x 992 = (1000 + 8)(1000 - 8)

1008 x 992 = 1000² - 8²

1008 x 992 = 1000000 - 64

1008 x 992 = 999936

(iv) Algebraic identify (a + b)(a - b)  = a² - b²

185² − 115² = (185 + 115)(185 - 115)

185² − 115² = (300)(70)

185² − 115² = 21000

Answer 2

Answer:

I) 10609

2)9216

3)9951

4)999936

5)21000