If m and n stand for integers then 2m and 2n stand for even integers. Use the distributive property to show that the sum of any two even numbers is even

Question

I need help please!

Answer 1

Hi Virginia;

2m+2n

Application of distributive property...

2(m+n)

You said that m and n are integers.  You also said that 2m and 2n are even integers.  This means that m and n are of the same character, odd or even.  An integer added to an integer of identical character, produces an even result.  Furthermore, an integer multiplied by an even integer such as 2, produces an even result.

 

I do not know what more to say about this to prove the point.

Answer 2

m and n stand for any integers that can be even or odd.

 

Any even number has a factor of 2, so (2m) and (2n) are both even.

 

2m + 2n = 2(m+n) by the distributive property.

 

Since 2(m+n) has a factor of 2 it is even, so the sum of even integers is even.