Question

How do you simplify $6a + 2a$ ?

Answer 1

Hint: First, we have to understand the concept of like terms. Like terms are terms that contain the same variables and that same variable must be raised to the same power that is the same variables must have the same degree value, but their numerical coefficient can be different. Take out the variable common and add the numerical coefficient in the expression.

Complete step-by-step solution:
The given expression is: $6a + 2a$
Analyze the expression and determine the variable and its power.
First-term is $6\;a$ , which contains a variable $a$ raised to the power one with the numerical coefficient $6$ .
The second term is $2\;a$ , which contains a variable $a$ raised to the power one with the numerical coefficient $2$ .
As both terms contain the same variable $a$ with the same degree which is one and with different numerical coefficients i.e. $6$ and $2$ respectively, so we can take variable $a$ common and add their coefficients to add the first and second terms of the expression.
$ \Rightarrow 6a + 2a$
Taking variable $a$ common from the first and second term of the expression, we get:
$ \Rightarrow a(6 + 2)$
By adding the numbers $6$ and $2$ , we get:
$ \Rightarrow a8$
As we know the product of two numbers that are $c$ and $d$ follow the commutative property, i.e. $c \times d = d \times c$ .
So we can write $a\;8$ as $8\;a$ , i.e.
$ \Rightarrow 8a$

This shows that on simplification the expression $6a + 2a$ is equal to $8\;a$

Note: There is an alternate method to simplify the given expression.
As we can see in the expression that the first term is nothing but $6$ times $a$ and the second term is nothing but $2$ times $a$ .
So we can write numbers of variables $a$ as a sum, i.e.
$6a = a + a + a + a + a + a$ and $2a = a + a$
$ \Rightarrow 6a + 2a = a + a + a + a + a + a + a + a$
That is the expression $6a + 2a$ contains $8$ times of $a$ .
$ \Rightarrow 6a + 2a = 8a$