Question

Evaluate each of the following using identities:
(i) (399)²(ii) (0.98)²
(iii) 991×1009
(iv) 117×83

Answer 1

$(400 - 1) {}^{2}$

$(400) {}^{2} - 2 \times 400 \times 1 + 1 {}^{2}$

160000-800+1

159201

Answer 2

(i) Given : (399)²

By using the identity, (a - b)² = a² + b² – 2ab

(399)² = (400 - 1)²

= 400² + 1² - 2 × 400 × 1

= 1600 + 1 - 800

= 1601 - 800

= 159201

(399)² = 159201

(ii) (0.98)²

By using the identity, (a - b)² = a² + b² – 2ab

(0.98)² = (1 - 0.02)²

= 1² + 0.02² - 2 × 1 × 0.02

= 1 + 0.0004 - 0.04

= 1.004 - 0.04

= 0.9604

(0.98)² = 0.9604

 

(iii) 991 × 1009

By using the identity, (a + b)(a - b) = a² - b²

991 × 1009 = (1000 - 9) (1000 + 9)

= 1000² - 9²

= 1000000 - 81

991 × 1009 = 999919

(iv) 117  ×  83

By using the identity, (a + b)(a - b) = a² - b²

117  ×  83 = (100 + 17) (100 - 17)

= 100² - 17²

= 10000 - 289

= 9711

117  ×  83 = 9711

HOPE THIS ANSWER WILL HELP YOU……

 

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