Question

How do you identify the terms, like terms, coefficients, and constant terms of the expression $4{{x}^{2}}+1-3{{x}^{2}}+5$ ?

Answer 1

Hint: A term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by +, - or $\div $ sign. Like terms are terms whose variables are same and the exponents of the variables are also similar. We can add or subtract like terms. Coefficients of a term are the constants which come along with the variables. Constant terms are those terms that do not contain variables.

Complete step-by-step answer:
We have to identify the terms, like terms, coefficients, and constant terms of the expression $4{{x}^{2}}+1-3{{x}^{2}}+5$ .We know that a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by +, - or $\div $ sign.
Hence, the terms in the given expression are
$4{{x}^{2}},1,3{{x}^{2}},5$
We know that like terms are terms whose variables are the same and the exponents of the variables are also similar. We can add or subtract like terms. Therefore, like terms in the given expression are
$4{{x}^{2}}\text{ and }3{{x}^{2}}$
$1\text{ and }5$
We know that coefficients of a term are the constants which come along with the variables. For example, in $a{{x}^{2}}$ , a is the coefficient of ${{x}^{2}}$ . Also in terms of the form $\left( a+b \right){{x}^{5}}$ , $\left( a+b \right)$ is the coefficient of ${{x}^{5}}$ . Therefore, the coefficients of the given expression are
$4$ in $4{{x}^{2}}$
$-3$ in $-3{{x}^{2}}$
Let us find the constant terms. Constant terms are those terms that do not contain variables. Therefore, 1 and 5 are constant terms.

Note: Students may get confused why constant terms are like terms. We can see that like terms can be added or subtracted. We can simplify the given expression by adding the like terms. We will get
$\left( 4{{x}^{2}}-3{{x}^{2}} \right)+\left( 1+5 \right)={{x}^{2}}+6$
Students must be careful to take the negative signs along with the constant terms as in $-3$ in $-3{{x}^{2}}$ .