Question

For the given expression,identify the terms, like terms, coefficients, and constant terms. Then simplify the expression.

$9+n-1-7n$

Short answer

Terms:$9,n,-1,-7n$

Like terms:$n\text{and}-7n;9\text{and}-1$

Coefficients:localid="1649121242529" $1,-7$

Constant term:localid="1649121260257" $9,-1$

The simplified expression is$8-6n$.

Step-by-step solution

Step-1 – Apply the concept of terms and like terms

In an algebraic expression, terms are separated by plus or minus signs.

The term coefficient refers to the number in front of the variable in any term of the expression.

A constantterm is the number which have no variable associated with it.

Like terms are the terms which have identical variable parts with same exponent on it. Constants are considered to be like terms as well.

Step-2 – Identify the terms

To identify the terms in the given expression$9+n-1-7n$, First rewrite it as a sum as,$9+n+(-1)+(-7n)$

Here observe that the terms$9,n,-1,\text{\hspace{0.17em}and}-7n$are separated by plus signs.

So, the terms of the given expression are$9,n,-1,-7n$$9,n,-1,-7n$.

Step-3 – Identify the like terms

The like terms are the terms which have identical variable with similar power on it.

Here in the given expression only variable terms are$n\text{and}-7n$, and both terms have the same variable. Also observe that there are two constant terms 9 and –1.

So, the like terms in the given expression are localid="1649121369660" $n\text{and}-7n;9\text{and}-1$.

Step-4 – Identify the coefficients

Coefficients are the numbers associated with the variable in any term of the expression.

In the given expression the variable terms are$n\text{and}-7n$only.

So, the coefficients in the given expression are 1 and –7.

Step-5 – Identify the constant term

Constant terms are the number in any expression which do not have any variable part.

In the given expression the numbers without variable part are 9 and –1.

So, the constant terms in the given expression are 9 and –1.

Step-6 – Simplify the expression

In order to simplify the given expression, group the like terms and combine them as shown below

$\begin{array}{c}9+n-1-7n=9-1+n-7n\\ =(9-1)+(1-7)n\\ =\left(8\right)+(-6)n\\ =8-6n\end{array}$

Thus, the simplified expression is$8-6n$