Question

How do you combine like terms in $5{{c}^{2}}+4{{c}^{2}}+6+2c+2c$?

Answer 1

Hint: We have to find the like terms in $5{{c}^{2}}+4{{c}^{2}}+6+2c+2c$ and then simplify them. We check the algebraic terms in the equation of $5{{c}^{2}}+4{{c}^{2}}+6+2c+2c$ and also the power values. Terms with same degree and same algebraic forms will be combined like terms.

Complete step-by-step solution:
In the equation of $5{{c}^{2}}+4{{c}^{2}}+6+2c+2c$, the only variable term is $c$.
There are three types of power or indices values for variable $c$.
The terms $5{{c}^{2}}$ and $4{{c}^{2}}$ are like terms as they have the same variable and the indices value is also the same which is 2.
Similarly, the terms $2c$ and $2c$ are like terms as they have the same variable and the indices value is also the same which is 1.
We now simplify the like terms using the binary operation between them.
We add $5{{c}^{2}}$ and $4{{c}^{2}}$ to get \[5{{c}^{2}}+4{{c}^{2}}=9{{c}^{2}}\].
Then we add $2c$ and $2c$ to get $2c+2c=4c$.
The combined solution will be
$\begin{align}
  & 5{{c}^{2}}+4{{c}^{2}}+6+2c+2c \\
 & =9{{c}^{2}}+6+4c \\
 & =9{{c}^{2}}+4c+6 \\
\end{align}$
This way we combine like terms in $5{{c}^{2}}+4{{c}^{2}}+6+2c+2c$ and get $9{{c}^{2}}+4c+6$.

Note: In the calculation we must be careful about the number of variables available in the terms. Unlike terms can be created with different variables but the same indices value. In compound terms we check the individual indices.