The Correct Answer and Explanation is:1
Correct Answer:
8pq + 3qr
Explanation:
The problem asks to simplify the given expression, 8pq + 3qr. In algebra, simplifying an expression often involves combining “like terms.” Like terms are terms that contain the exact same variables raised to the exact same powers. The numerical coefficients of the terms can be different.
Let’s analyze the expression 8pq + 3qr. This expression consists of two terms:
- The first term is 8pq. The coefficient is 8, and the variable part is pq.
- The second term is 3qr. The coefficient is 3, and the variable part is qr.
To determine if these two terms can be added together, we must check if they are like terms. We compare their variable parts: pq and qr. Although both terms share the variable q, they are not identical. The first term contains the variable p, while the second term contains the variable r. Since the set of variables in each term is different (p and q vs. q and r), they are not like terms.
Because 8pq and 3qr are not like terms, they cannot be combined into a single term through addition. Therefore, the expression is already in its simplest form.
It is worth noting that the question refers to the expression as a “monomial.” A monomial is an algebraic expression consisting of only one term. The expression 8pq + 3qr actually contains two terms, which makes it a binomial. Regardless of this terminology, the process of simplification remains the same, and the expression cannot be reduced further. The final simplified form is the expression as it was originally given.
