Find the value of:
(i) (82)2 − (18)2
(ii) (128)2 − (72)2
(iii) 197 × 203
(iv) $\frac{198 \times 198-102 \times 102}{96}$
(v) (14.7 × 15.3)
(vi) (8.63)2 − (1.37)2
We shall use the identity $(a-b)(a+b)=a^{2}-b^{2}$.
(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) $(128)^{2}-(72)^{2}$
$=(128-72)(128+72)$
$=(56)(200)$
$=11200$
(iv) $\frac{198 \times 198-102 \times 102}{96}$
$=\frac{(198)^{2}-(102)^{2}}{96}$
$=\frac{(198-102)(198+102)}{96}$
$=\frac{(96)(300)}{96}$
$=300$
(v) $(14.7 \times 15.3)$
$=(15-0.3) \times(15+0.3)$
$=(15)^{2}-(0.3)^{2}$
$=225-0.09$
$=224.91$
(vi) $(8.63)^{2}-(1.37)^{2}$
$=(8.63-1.37)(8.63+1.37)$
$=(7.26)(10)$
$=72.6$
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