Question
Monomial algebraic expression is - \( \begin{array}{ll}\text { (a) } 4 x & \text { (b) } 4 x+3 y \\ \text { (c) } 3 x+2 y & \text { (d) } 3 x+2 y+5 z\end{array} \)
Ask by Hampton Hills. in India
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 4x \) is a monomial.
Solution
A monomial is an algebraic expression that contains only one term. This term can be a constant, a variable, or a product of a constant and variables raised to nonnegative integer powers.
- Option \( (a) \) is \( 4x \), which is a single term.
- Option \( (b) \) is \( 4x + 3y \); this has two terms.
- Option \( (c) \) is \( 3x + 2y \); this also has two terms.
- Option \( (d) \) is \( 3x + 2y + 5z \); this consists of three terms.
Since only one term qualifies as a monomial, the correct answer is
\( (a)\ 4x \).
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Simplify this solution The Deep Dive
A monomial algebraic expression consists of a single term that includes a coefficient and variable(s), without any addition or subtraction of separate terms. So, from the options provided, \(4x\) is the only monomial since it represents a single term. Monomials can be expanded into more complex polynomials by introducing more variables and coefficients, which leads to fascinating mathematical concepts. For instance, if you take the monomial \(4x\) and multiply it with \(3y\), you get a product of \(12xy\), expanding your algebraic expression into a binomial! This transformation is the basis for polynomial equations, opening doors to complex problem-solving in algebra.
