Question

State, true or false:
(i) product of two different integers can be zero.
(ii) product of 120 negative integers and 121 positive integers is negative.
(iii) $a\times (b+c)=a\times b+c$
(iv) $(b-c)\times a=b-c\times a.$

Answer 1

(i) True.
Example:$5\times 0,0\times -8=0$
(ii) False.
The total number of negative integers is 120 which is an even number and we know that the product of even numbers of negative integers is always positive. Hence, the sign of the product will be positive.
(iii) False.
$a\times (b+c)\ne a\times b+c$
$ab+ac\ne ab+c$
(iv) False.
$(b-c)\times a\ne b-c\times a$
$ab-ac\ne b-ca$