Q14. - Algebra 2

Question

Simplify each expression

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

Step-by-Step Solution

Answer

$9p-2n+4p+2n$ is simplified to $13p$ 

Step 1 - 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	$a\left(b+c\right)=ab+ac\text{ and }\left(b+c\right)a=ba+ca$

Step 2 - 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

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

Step 3 - Use additive identity property

Simplify parentheses by adding the terms as shown below

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