Theory:

While multiplying \(2\) integers, depending upon the sign of the two or more than two numbers, the answer can change.
  
1. Any one number has a negative sign:
In multiplication operation, if any one of the numbers is negative, then the result will have a negative sign \((+ve) × (-ve) = -ve\).
Example:
1. 235×(-5)=-1175
 
2. (-92)×(-16)=1472
 
3. 3×(-16)=-48
2. Both numbers have a negative sign:
In multiplication operation, when both the numbers are negative, then the result will have a positive sign \((-ve)×(-ve) = +ve\). This is according to the great mathematician Euler who proved, \((-1)×(-1)=+1\).
Example:
1. \((-9) × (-10) = 90\)
 
2. \((-12) × (-6) = 72\)
 
3. \((-10) × (-10) = 100\)
 
4. \((-5) × (-5) = 25\)
3. Both numbers have positive sign:
In multiplication, when both the numbers are positive, the result will be a positive sign \((+ve) × (+ve) =+ve\)
Example:
1. \(12 × 10 = 120\)
 
2. \(10 × 6 = 60\)
 
3. \(10 × 5 = 50\)
 
4. \(8 × 6 = 48\)
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Multiplication with zero:
Any integer \(×\) \(0 = 0\). Irrespective of nature and sign of integer, when an integer is multiplied by zero, the result is \(0\).
Example:
1. \(40 × 0 = 0\)
 
2. −92 \(× 0 =\) 0