Question

Find the value 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) $(14.5\times 15.3)$
(vi) $(8.63{)}^2-(1.37{)}^2$

Answer 1

i)

$(82{)}^2-(18{)}^2(\text{using}{a}^2-b^2=(a+b\left)\right(a-b\left)\right)$

$=(82+18)(82-18)$

$=100\times 64=6400$

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)

$(14.5\times 15.3)=221.85$

vi)

$(8.63{)}^2-(1.37{)}^2$

$=(8.63+1.37)(8.63-1.37)$

$=10\times 7.26$

$=72.6$