Evaluate :

Using expansion of $(a + b)^{2} o r (a - b)^{2}$

(i) $(208)^{2}$

(ii) $(92)^{2}$

(iii) $(415)^{2}$

(iv) $(188)^{2}$

(v) $(9.4)^{2}$

(vi) $(20.7)^{2}$

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Solution

(i) $(208)^{2} = (200 + 8)^{2}$

$= (200)^{2} + (8)^{2} + 2 (200) (8) = 40000 + 64 + 3200 = 43264$

(ii) $(92)^{2} = (100 - 8)^{2} = (100)^{2} + (8)^{2} - 2 (100) (8) = 10000 + 64 - 1600 = 10064 - 1600 = 8464$

(iii) $(415)^{2} = (400 + 15)^{2} = (400)^{2} + (15)^{2} + 2 (400) (15) = 160000 + 225 + 12000 = 172225$

(iv) $(188)^{2} = (200 - 12)^{2} = (200)^{2} + (12)^{2} - 2 (200) (12) = 40000 + 144 - 4800 = 40144 - 4800 = 35344$

(v) $(9.4)^{2} = (10 - .6)^{2} = (10)^{2} + (.6)^{2} - 2 (10) (.6) = 100 + .36 - 12 = 88 + .36 = 88.36$

(vi) $(20.7)^{2} = (20 + .7)^{2} = (20)^{2} + (.7)^{2} + 2 (20) (.7) = 400 + .49 + 28 = 428 + .49 = 428.49$

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