Question

Using $a^2-b^2=(a+b)(a-b)$, find
(i) ${51}^2-{49}^2$
(ii) ${1.02}^2-{0.98}^2$
(iii) ${153}^2-{147}^2$
(iv) ${12.1}^2-{7.9}^2$

Answer 1

i) ${51}^2-{49}^2$

$=(51-49)(51+49)$

$=2\times 100$

$=200$

ii) $(1.02{)}^2-(0.98{)}^2$

$=(1.02-0.98)(1.02+0.98)$

$=0.04\times 2$

$=0.08$

iii) ${153}^2-{147}^2$

$=(153-147)(153+147)$

$=6\times 300$

$=1800$

iv) ${12.1}^2-{7.9}^2$

$=(12.1-7.9)(12.1+7.9)$

$=4.2\times 20$

$=8.4$