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Addition

Gareth56
in Linear Algebra and Group Theory

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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

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.

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

 

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

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