Question

How do you simplify $2b - 6 + 3b - b?$

Answer 1

Hint: The given expression is consist of one variable and constant, to simplify the given expression, first with the help of commutative property of addition, group the similar terms that is all variables in a group or parentheses and constants in a group then perform the algebraic operation the expression has and finally see if there is any common factor between the terms of the expression if yes then take out the common factor and if no then congratulations you have simplified the expression.

Complete step by step solution:
In order to simplify the given expression $2b - 6 + 3b - b$, we will first use the commutative property of addition to group similar terms in the expression as follows
$ \Rightarrow 2b - 6 + 3b - b$
We can write this expression as
$ \Rightarrow 2b + ( - 6) + 3b + ( - b)$
Now, we can use commutative property of addition here in the above equation as follows
$
    \Rightarrow 2b + ( - 6) + 3b + ( - b) \\
    \Rightarrow \left( {2b + 3b + ( - b)} \right) + ( - 6) \\
 $
Simplifying it further by doing the algebraic operations between similar terms, we will get
$ \Rightarrow \left( {2b + 3b + - b} \right) - 6$
According to BODMAS rule, we will first perform addition
$ \Rightarrow \left( {5b - b} \right) - 6$
Now, doing subtraction, we will get
$ \Rightarrow 4b - 6$
Here in the above expression, we will check for any common factor between all terms of the expression
$
 \Rightarrow 4b = 2 \times 2 \times b \\
 \Rightarrow 6 = 2 \times 3 \\
 $
We can see that $2$ is a common factor between both terms, so taking it out, we will get
$ = 2(2b - 3)$
Therefore $2(2b - 3)$ is the simplified form of the given expression.

Note: We have written $ - 6\;{\text{and}}\; - b\;{\text{as}}\; + ( - 6)\;{\text{and}}\; + ( - b)$ because in order to use commutative property, commutative property holds true only for addition and multiplication operation, so we have changed the above subtraction into addition of negative numbers or variables to use commutative property.