Question
Question 25 of 25 Which of these is a binomial? A. \( 2 x^{3}-7 y^{3} \) B. \( x+2 y^{2}-7 \) C. \( a b \) D. \( 5 x y \)
Ask by Floyd Hampton. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Option A is a binomial.
Solution
To determine which of the given options is a **binomial**, we need to recall that a binomial is an algebraic expression consisting of exactly **two terms**.
Let's analyze each option:
**A. \( 2x^{3} - 7y^{3} \)**
- This expression has **two terms**: \( 2x^{3} \) and \( -7y^{3} \).
- **Binomial**
**B. \( x + 2y^{2} - 7 \)**
- This expression has **three terms**: \( x \), \( 2y^{2} \), and \( -7 \).
- **Not a binomial**
**C. \( ab \)**
- This is a **single term**.
- **Not a binomial**
**D. \( 5xy \)**
- This is also a **single term**.
- **Not a binomial**
**Conclusion:**
**Option A** is the only binomial among the choices provided.
**Answer:**
A. \( 2 x^{3}-7 y^{3} \)
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Simplify this solution Extra Insights
A binomial is a polynomial that consists of exactly two terms. Both options C and D fit this definition, as they each have two different terms. \( a b \) is made up of two variables multiplied together, while \( 5 x y \) contains the coefficient 5 multiplied by two variables \( x \) and \( y \). Therefore, both C and D are correct answers. When identifying binomials, keep an eye out for the number of distinct terms. A fun tip is to look for plus or minus signs separating the terms—these are your clues. A common mistake is to miscount or overlook coefficients that signal separate terms.
