Addition

[Gareth56]

Can I ask why for example:-

 

8a^5 b^5 + 10a^5 b^5 = 18a^5 b^5 and not 18a^10 b^10

 

Thanks

[timo]

Two possible answers:

1) Why should it?

2) That's what the distributive property of the real numbers is like: 3x + 2x = (3+2)x = 5x hence 8a^5 + 10a^5 = (8 + 10)a^5 = 18a^5.

[Bignose]

Atheist has it spot on.

 

Put some numbers in there to show it to be wrong.

 

Let a^5 = 7 and let b^5 = 10

 

8*7*5 + 10*7*5 = 280 + 350 = 630 = 18*7*5

 

Not 18*(7*7)*(5*5) = 22050

[DrP]

Had it been a multiplication you would add the powers though:

 

8a^5 b^5 X 10a^5 b^5 = 80a^10 b^10