Find the value of:

Question:

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

Solution:

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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