Evaluate each of the following by using identities: (i)`95 xx 96` (ii) `104xx 96` (iii) `105 xx 106`

Explanation

(i)`95xx96=(100-5)(100-4)`
=By using identity `(x+a)(x+b)=(x^2+(b+a)x +ab)`
`=10000-900+20`
`=9120`
(ii) `104 xx 96`
Identity: `(a + b)(a - b) = a^2 - b^2`
`104 xx 96 = (100 + 4)(100 - 4)`
Substituting `a = 100, b = 4` in the above identity, we get
`= (100)^2 - (4)^2`
`= 10000 -16`
`= 9984`
(iii)`(100+5)(100+6)`
`=10000+1100+30` [using above identity]
`=11130`