Question

Simplify the following using brackets.(a) 105 x 104(b) 103 x 85(c) 60 x 108(d) 92 x 106​

Answer 1

Answer:

1. 105*104=(100+5) (100+4)

By using identity = (x+a) (x+b)

= x^2 +(a+b)x +ab

=(100)^2 +(5+4)*100 +5*4

=10000+(9)*100+20

=10000+900+20

= 10920 ans.

2. 103*85=(80+23) (80+5)

By using identity= (x+a) (x+b)

=(80)^2+(23+5)*80+23*5

=6400+(28)*80+115

= 6400+2240+115

=8640+115

=8755 ans.

3. 60*108=(55+5) (55+53)

By using identity =(x+a) (x+b)

=(55)^2+(5+53)*55+5*53

=3025+(58)*55 + 265

=3025 + 4190+265

=7215+265

= 7480 ans.

4. 92*106 = (100-6) (100+6)

By using identity= (x+y) (x-y)

=( x)^2-(y)^2

=(100)^2-(6)^2

=10000-36

=9964 ans.

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