Question

Find the values of
(i) $(82{)}^2-(18{)}^2$
(ii) $(128{)}^2-(72{)}^2$
(iii) $197\times 203$
(iv) $\frac{198\times 198-102\times 102}{96}$
(v) $(14.7\times 15.3)$
(vi) $(8.63{)}^2-(1.37{)}^2$

Answer 1

(i) $(82{)}^2-(18{)}^2=(82+18)(82-18)=100\times 64=6400$

(ii) $(128{)}^2-(72{)}^2=(128+72)(128-72)=200\times 56=11200$

(iii) $197\times 203=(200-3)(200+3)=(200{)}^2-(3{)}^2=40000-9=39991$

(iv) $\frac{198\times 198-102\times 102}{96}=\frac{(198{)}^2-(102{)}^2}{96}=\frac{(198+102)(198-102)}{96}=\frac{300\times 96}{96}=300$

(v) $(14.7\times 15.3)=(15-0.3)(15+0.3)=(15{)}^2-(0.3{)}^2=225-0.09=224.01$

(vi) $(8.63{)}^2-(1.37{)}^2=(8.63+1.37)(8.63-1.37)=10.00\times 7.26=72.6$