Question

evaluate without multiplying directly :1) 103*107 2)95*96 3)104*96

Answer 1

1.) 103×107
(105-2)(105+2)
(105^2-2^2)
11025-4
11021

2.) 95×96
(95.5-0.5)(95+0.5)
(95.5^2-0.5^2)
9120.25-0.25
9120


3.)104×96
(100+4)(100-4)
(100^2-4^2)
10000-16
9984

Answer 2

1) 103 x 104
SOLUTION] (100+3) x (100+4)
 By using identity : (x+a)(x+b) = $x^{2} + (a+b) X x + ab$
                 => $100^{2} + (7+3) X 100 + (3 X 7)$
                 => 10000 + 1000 + 21
                 =>11021 [ANS]

2) 95 x 96
SOLUTION] (100-5) x (100-4)
By using identity : (x+a)(x+b) = $x^{2} + (a+b) X x + ab$
                 => $100^{2} + {(-5)+(-4)} X 100 + (-5 X -4)$
                 => 10000 + (-900) + 20
                 => 10000 - 900 + 20
                 => 9120 [ANS]

3) 104 x 96 
SOLUTION] (100+4) x (100-4)
By using identity: (x+y)(x-y) = $x^{2} - y^{2}$
                 => $100^{2} - 4^{2}$
                 => 10000 -16
                 => 9984 [ANS]

HOPE IT HELPED YOU !!! IF SO, PLEASE MARK IT AS BRAINLIEST ;)