Answer :
To determine whether two terms are like terms, we must check if they have the same variable raised to the same power. Let's analyze each pair:
1. For the first pair, consider the terms
[tex]$$7x^2 \quad\text{and}\quad 1x^3.$$[/tex]
Although both contain the variable [tex]$x$[/tex], the exponents are [tex]$2$[/tex] and [tex]$3$[/tex], respectively. Since the exponents are different, these are not like terms.
2. For the second pair, consider the terms
[tex]$$3x \quad\text{and}\quad 3x^3.$$[/tex]
Here, [tex]$3x$[/tex] can be thought of as [tex]$3x^1$[/tex]. Comparing the exponents [tex]$1$[/tex] and [tex]$3$[/tex], they are not the same, so these terms are not like terms.
3. For the third pair, consider the terms
[tex]$$4x^3 \quad\text{and}\quad 2x^3.$$[/tex]
Both terms have the variable [tex]$x$[/tex] raised to the same exponent, [tex]$3$[/tex]. Therefore, these terms are like terms.
4. For the fourth pair, consider the terms
[tex]$$2x^4 \quad\text{and}\quad 2.$$[/tex]
The constant term [tex]$2$[/tex] can be considered as [tex]$2x^0$[/tex] (since any number is equivalent to the number times [tex]$x^0$[/tex]). Comparing the exponents [tex]$4$[/tex] and [tex]$0$[/tex], they are different. Hence, these are not like terms.
In conclusion, among the given pairs, only the third pair ([tex]$4x^3$[/tex] and [tex]$2x^3$[/tex]) are like terms.
Final Answer: Only pair 3 represents like terms.
1. For the first pair, consider the terms
[tex]$$7x^2 \quad\text{and}\quad 1x^3.$$[/tex]
Although both contain the variable [tex]$x$[/tex], the exponents are [tex]$2$[/tex] and [tex]$3$[/tex], respectively. Since the exponents are different, these are not like terms.
2. For the second pair, consider the terms
[tex]$$3x \quad\text{and}\quad 3x^3.$$[/tex]
Here, [tex]$3x$[/tex] can be thought of as [tex]$3x^1$[/tex]. Comparing the exponents [tex]$1$[/tex] and [tex]$3$[/tex], they are not the same, so these terms are not like terms.
3. For the third pair, consider the terms
[tex]$$4x^3 \quad\text{and}\quad 2x^3.$$[/tex]
Both terms have the variable [tex]$x$[/tex] raised to the same exponent, [tex]$3$[/tex]. Therefore, these terms are like terms.
4. For the fourth pair, consider the terms
[tex]$$2x^4 \quad\text{and}\quad 2.$$[/tex]
The constant term [tex]$2$[/tex] can be considered as [tex]$2x^0$[/tex] (since any number is equivalent to the number times [tex]$x^0$[/tex]). Comparing the exponents [tex]$4$[/tex] and [tex]$0$[/tex], they are different. Hence, these are not like terms.
In conclusion, among the given pairs, only the third pair ([tex]$4x^3$[/tex] and [tex]$2x^3$[/tex]) are like terms.
Final Answer: Only pair 3 represents like terms.
