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Mathematics

Evaluate using expansion of (a + b)2 or (a - b)2 :

(i) (208)2

(ii) (92)2

(iii) (9.4)2

(iv) (20.7)2

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Answer

(i) (208)2

(200 + 8)2

Using the formula

(∵ (x + y)2 = x2 + 2xy + y2)

= (200)2 + 2 x 200 x 8 + (8)2

= 40000 + 3200 + 64

= 43264

Hence, (208)2 = 43264

(ii) (92)2

(100 - 8)2

Using the formula

(∵ (x - y)2 = x2 - 2xy + y2)

= (100)2 - 2 x 100 x 8 + (8)2

= 10000 - 1600 + 64

= 8400 + 64

= 8464

Hence, (92)2 = 8464

(iii) (9.4)2

(10 - 0.6)2

Using the formula

(∵ (x - y)2 = x2 - 2xy + y2)

= (10)2 - 2 x 10 x 0.6 + (0.6)2

= 100 - 12 + 0.36

= 88 + 0.36

= 88.36

Hence, (9.4)2 = 88.36

(iv) (20.7)2

(20 + 0.7)2

Using the formula

(∵ (x + y)2 = x2 + 2xy + y2)

= (20)2 + 2 x 20 x 0.7 + (0.7)2

= 400 + 28 + 0.49

= 428 + 0.49

= 428.49

Hence, (20.7)2 = 428.49

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