Using Properties of Real Numbers: Justifying Equalities

[paulmdrdo1]

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

 

[topsquark]

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

 

[Evgeny.Makarov]

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.