Find the squares of the following numbers using the identity `(a-b)^2=a^2-2a b+b^2:\ ` (I)395 (ii) 995 (iii) 495 (iv) 498 (v)99 (vi) 999 (vii) 599

Explanation

(1)`(395)^2=(400-5)^2`
`=(400)^2+(5)^2-2xx400xx5`
`=160000+25-4000`
`=156025`
(ii)`995^2=(1000-5)^2`
`=(1000)^2+(5)^2-2xx1000xx5`
`=1000000+25-10000`
`=990025`
(iii)`(495)^2=(500-5)^2`
`=(500)^2+(5)^2-2xx500xx5`
`=250000+25-5000`
`=245025`
(iv)`(498)^2=(500-2)^2`
`=(500)^2+(2)^2-2xx500xx2`
`=250000+4-5000`
`=248004`
(v)`99^2=(100-1)^2`
`=(100)^2+(1)^2-2xx100xx1`
`=10000+1+200`
`=9801`
(vi)`(999)^2=(1000-1)^2`
`=(1000)^2+(1)^2-2xx1000xx1`
`=1000000+1-2000`
`=998001`
(vii)`(599)^2=(600-1)^2`
`=(600)^2+(1)^2-2xx600xx1`
`=360000+1-1200`
`=358801`