Question

Evaluate the following products without multiplying directly:
1. 95×96
2. 104×96

Answer 1

1)95x96
95=100-5
96=100-4
$< x + a > < x + b > {x}^{2} + (a + b)x + ab$
${100}^{2} + {( - 5) + ( - 4)}100 + {( - 5) x ( - 4)}$
=10000+(-9)100+20
=10000-900+20
=9100+20
=9120

2)104x96
104=100+4
96=100-4
(a+b)(a-b) ={a}^(2)-{b}^(2)
(100+4)(100-4)={100}^(2)-{4}^(2)
=10000-16
=9984

hope it helps....

Answer 2

Answer:

1. 95×96

= (90+5)×(90+6)

= (90²)+(5+6)(90)+(5×6)

=8100+990+30

=9120...