MHB Using Properties of Real Numbers: Justifying Equalities

AI Thread Summary
The discussion focuses on justifying equalities using properties of real numbers. Participants emphasize the importance of the associative and commutative laws for addition in simplifying expressions. There is a mention of a typo regarding a missing term in one of the equations. Additionally, it is suggested that studying the axioms of real numbers is essential for understanding the justification process. Overall, the conversation highlights the need for clarity in applying mathematical properties to validate equalities.
paulmdrdo1
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justify each of the steps in the following equalities.

i don't know where to start. what i know is i have to use properties of real numbers. please help!

1. $\displaystyle \left ( x+3 \right )\left(x+2\right)\,=\,\left ( x+3 \right )x+\left ( x+3 \right )2\,=\,\left ( x^2+3x \right )+\left ( 2x+3*2 \right ) $

2. $\displaystyle \left(3x^2+2\right)+\left(x^2+2x\right)\,=\,\left(\left (3x^2+2\right)+x^2\right)\,=\,\left(x^2+\left(3x^2+2\right)\right)+2x$
 
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paulmdrdo said:
2. $\displaystyle \left(3x^2+2\right)+\left(x^2+2x\right)\,=\,\left(\left (3x^2+2\right)+x^2\right)\,=\,\left(x^2+\left(3x^2+2\right)\right)+2x$
Apart from missing the 2x term in the middle expression (a typo I presume) this is just regrouping using the associative and commutative laws for addition.

-Dan
 
I am not sure which properties are meant, but you probably should study the axioms of real numbers (see, e.g., http://www.calvin.edu/~rpruim/courses/m361/F03/overheads/real-axioms-print-pp4.pdf). Then study https://driven2services.com/staging/mh/index.php?threads/5700/. For each equality, you have to say which axiom is used.
 
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