Using identities, evaluate.
(i) `71^2`
(ii) `99^2`
(iii) `102^2`
(iv) `998^2`
(v) `5.2^2`
(vi) `297 xx 303`
(vii) `78 xx 82`
(viii) `892`
(ix) `105 xx 95`

Explanation

(i) `71^2 = (70+1)^2`
`(70)^2 + 2(70)(1) + (1)^2`
`= 4900+ 140+ 1 = 5041`
(ii) `99^2 = (100-1)^2`
`= 100^2 - 2(100)(1) + 1`
`= 10000 - 200 +1`
`= 9801`
(iii) `102^2 = (100+2)^2`
`= 100^2 + 2^2 + 2*2*100 = 200 + 4+ 400= 604`
(iv) `998^2 = (100-2)^2`
`= 100^2 + 2^2 - 2*2*100 = -200 + 4 = -196`
(v) `5.2^2 = (5+ 0.2)^2`
`= 5^2 + 0.2^2 + 2(0.2)(5)`
`= 25 + 0.04 + 2= 27.04`
(vi) `297 xx 303 = (300-3) xx (300 +3)`
`= (300)^2 - 3^2`
`= 90000-9= 89991`
(vii)`78 xx 82 = (80-2)(80+2)`
`(80)^2 - (2)^2 = 6400 - 4= 6396`
(viii) `8.9^ 2 = (9-0.1)^2`
`= 9^2 + 0.1^2 - 2(0.1)(9)`
`= 81 + 0.01 - 1.8`
`= 79.21`

(ix) `1.05 xx 9.5`
`105/100 xx 95/100`
`=((100+5)(100-5))/1000`
`= (100^2- 5^2 )/1000`
`= (10000-25)/1000`
`= 9975/1000 = 9.975`