Question

Evaluate the following products without multiplying directly:
i 103×107​

Answer 1

Here is your solution

Evaluate the following products without multiplying directly

(i)103×107  

(100 + 3) (100 + 7)

Now, by using identity :-

(x + a) (x + b) = x² + (a+b)*x + ab

x = 100 , a = 3 , b = 7

Now put value of x , a & b

=> (100)² + (3+7)*100 + (3*7)

=> 10000 + 1000 + 21

=> 11021

(ii)95×96  

(90 + 5) (90 + 6)

by using identity :-

(x + a) (x + b) = x² + (a+b)*x + ab

x = 90 , a = 5 , b = 6

Now put value of x , a & b

=> (90)² + (5+6)*90 + (5*6)

=> 8100 + 990 + 30

=> 9120

(iii)104×96  

(100 + 4) (100 - 4)

by using identity :-

(x + a) (x + b) = x² + (a+b)*x + ab

x = 100 , a = 4 , b = (-4)

now put value of x , a & b

=> (100)² + { 4 + (-4) }*100 + 4*(-4)

=> 10000 + (4 - 4)*100 - 16

=> 10000 + 0*100 - 16

=> 10000 - 16

=> 9984

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