Question #350985

3.1. If R is a ring and a, b, c, d ∈ R, evaluate (a + b)(c + d).

3.2. Prove that if a, b ∈ R, then (a + b)2 = a2 + ab + ba + b2 where

by x2 we mean xx.


1
Expert's answer
2022-06-16T09:16:14-0400

3.1

(a+b)(c+d)=a(c+d)+b(c+d)(a + b)(c + d) = a(c + d) + b(c + d)

by distributive law:

=(ac+ad)+(bc+bd)=ac+ad+bc+bd= (ac + ad) + (bc + bd) = ac + ad + bc + bd


3.2

(a+b)2=(a+b)(a+b)=a(a+b)+b(a+b)=a2+ab+ba+b2(a + b)^2 = (a + b)(a + b) = a(a + b) + b(a + b)=a^2 + ab + ba + b^2

Note that if R is not a commutative ring abbaab\ne ba


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS