# Properties of real numbers

#### paulmdrdo

##### Active member
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
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
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.