Question:`935421 xx 625` 

`=935421 xx 25 xx 25`
`=935421 xx 100/4 xx 100/4 `
`=(9354210000)/16`
 =584638125

Question:Use the formula,`(a^2+b^2+2ab)=(a+b)^2`
`387 xx 387 xx +114 +2 xx 387 xx 114` 

`=(387)^2 + (114)^2 + 2 xx 387 xx 114`
`=(387 + 114)^2=(501)^2=(500 + 1)^2`
 `=(500)^2 + (1)^2 + 2 xx 500 xx 1`
`=250000 + 1 + 1000
  =251001

Question:`1014 xx 986` 

`=(1000 + 14) xx (1000-14)`
`=(1000)^2 - (14)^2`
`=(1000000-196)=999804`

Question:`1299 xx 1299` 

`=(1299)^2=(1300-1)^2`
`=(1300)^2 + (1)^2 -2 xx 1300 xx 1`
 =1690000 + 1 - 2600=1687401

Question:`2(a^2 +b^2)` 

`(a+b)^2 +(a - b)^2`
:.`2 [(106)^2 + (94)^2] =[(106 + 94)^2 + (106 - 94)^2]`
`=[(200)^2 + (12)^2]`=40000 + 144=40144
So,`[(106)^2 + (94)^2 ]`=20072.

Question:`5358 xx 51` 

`5358 xx (50 + 1)`
`=(5358 xx 50) + (5358 xx 1)`
  =267900 + 5358=273258.

Question:`1307 xx 1307` 

`=(1307)^2`=`(1300 + 7)^2`
`=(1300)^2 + (7)^2 + 2 xx 1300 xx 7`
=1690000 + 49 + 18200
=1708249.

Question:Requred digit 

=unit digit in the product `(4 xx 8 xx 7 xx 3)`=2

Question:`9 xx 6 xx 4`216. 

In order to obtain 2 at the unit place it must be multiplied by a number whose unit digit is 7.
So,*must be replace by 7.

Question:Unit digit in `7^4`is 1.` 

:.Unit digit in `7^68`is 1.

 :.Unit digit in `7^71`is 3. `[1 xx 7 xx 7 xx 7` gives unit digit 3]

 Again,every power of 6 will give unit digit 6.

 :. Unit digit in `6^59` is 6.

 Clearly,unit digit in `3^4` is 1.

 So,unit digit in `3^64` is 1

 :.Unit digit in `3^65` is 3.

 :. Unit digit in `(7^71 xx 6^59 xx 3^65)` is 4. `[3 xx 6 xx 3`gives unit digit 4]`