Question

Simplify each expression

14. $9p-2n+4p+2n$

Short answer

$9p-2n+4p+2n$ is simplified to $13p$

Step-by-step solution

- Write properties of real numbers 

Properties of real numbers are written in following table:

For any real numbers a, b, and c:
Property	Addition	Multiplication
Commutative	$a+b=b+a$	$a·b=b·a$
Associative	$\left(a+b\right)+c=a+\left(b+c\right)$	$\left(a·b\right)·c=a·\left(b·c\right)$
Identity	$a+0=a=0+a$	$a·1=a=1·a$
Inverse	$a+\left(-a\right)=0=\left(-a\right)+a$	If $a\ne 0$, then $a·\frac{1}{a}=1=\frac{1}{a}·a$
Distributive	$a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$

- Simplify by grouping same variables

To simplify given equation, first use commutative property of addition between two middle most terms then distributive property to group coefficients of same variable as shown below

$\begin{array}{c}9p-2n+4p+2n=9p+4p-2n+2n\\ =\left(9+4\right)p+\left(-2+2\right)n\end{array}$

- Use additive identity property 

Simplify parentheses by adding the terms as shown below

$\begin{array}{c}\left(9+4\right)p+\left(-2+2\right)n=13p+0n\\ =13p\end{array}$