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Question

Find the value of:
(i) (82)2 − (18)2
(ii) (128)2 − (72)2
(iii) 197 × 203
(iv) 198×198-102×10296
(v) (14.7 × 15.3)
(vi) (8.63)2 − (1.37)2

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Solution

We shall use the identity (a-b) (a+b)=a2 - b2.

(i)
(82)2-(18)2=(82-18)(82+18)=(64)(100)=6400

(ii)
(128)2-(72)2=(128-72)(128+72)=(56)(200)=11200

(iii)
197×203=(200-3)(200+3)=2002-32=40000-9=39991

(iv)
198×198-102×10296=1982-102296=(198-102)(198+102)96=(96)(300)96=300

(v)
(14.7×15.3)=(15-0.3)×(15+0.3)=(15)2-(0.3)2=225-0.09=224.91

(vi)
(8.63)2-(1.37)2=(8.63-1.37)(8.63+1.37)=(7.26)(10)=72.6

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