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Properties of real numbers

paulmdrdo

Active member
May 13, 2013
386
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

Well-known member
MHB Math Helper
Aug 30, 2012
1,143
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

Well-known member
MHB Math Scholar
Jan 30, 2012
2,504
I am not sure which properties are meant, but you probably should study the axioms of real numbers (see, e.g., this PDF document). Then study this thread. For each equality, you have to say which axiom is used.