Note: i finished the first part, i jus need w the second part !
which of the equations from part a represent adding two rational numbers? what hypothesis can you make about the sum of two rational numbers? will the addition result in a rational or an irrational number? similarly, which equations represent the sum of a rational and an irrational number? what hypothesis can you make about the sum of an irrational and a rational number?

  see below

Step-by-step explanation:

Which of the equations from part A represent adding two rational numbers?

  Equations A, C, E

What hypothesis can you make about the sum of two rational numbers?

  The sum of two rationals will always be rational

Will the addition result in a rational or an irrational number?

  Our hypothesis is that the result is always rational. This can be justified by the fact that the sum of two rationals a/b + c/d, where a, b, c, d are integers and bd≠0, is (ad+bc)/(bd), a rational, based on closure of integers for multiplication and addition.

Which equations represent the sum of a rational and an irrational number?

  Equations B, F

What hypothesis can you make about the sum of an irrational and a rational number?

  The sum of a rational and irrational number is always irrational.

show us the picture

step-by-step explanation:

show the !

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18