Property `a`*`(b`*`c)=(a`*`b)`*`c` is called

Let P(x)=((x-a)(x-b))/((c-a)(c-b))c^(2)+((x-b)(x-c))/((a-b)(a-c))a^(2)+((x-c)(x-a))/((b-c)(b-a))b^(2) Prove that P(x) has the property that P(y)=y^(2) for all y in R .

Property 7 If abc are integers then ( i )a>b rArr a+c>b+c( ii) a

Property 5 Let ab and c be whole numbers and b!=0c!=0. If a-:b=c then b xx c=a

Property 6 Let ab and c be whole numbers and b!=0c!=0. If b xx c=0 then a-:c=b and a-:b=c

Let a, b, c be the three rational numbers where a=(2)/(3),b=(4)/(5) and c= -(5)/(6) Verify: (i) a + (b + c) = (a + b) +c (Associative property of addition) (ii) a xx (b xx c) = (a xx b) xx c (Associative property of multiplication)

The reaction in the conversion of (B) to (C ) is called:

CLoSURE PROPERTY If (a)/(b) and (c)/(d) are any two rational numbers then (a)/(b)-(c)/(d) is a rational number.

Properties I If (a)/(b) and (c)/(d) are two rational numbers such that (c)/(d)!=0 then (a)/(b)-:(c)/(d) is always a rational number.