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The question aims to write the algebraic expression of the given phrase. Algebraic expressions are the way of representing numbers using letters or alphabets without showing their actual values. The basics of algebra tell us how to define an unknown value using letters like x, y, z, etc. These letters are called variables here. Both variables and constants are used to make an algebraic expression.
A coefficient is a value placed before a variable and multiplied by the variable. In mathematics, an algebraic expression is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
For example, suppose James and Natalie were playing with matches and thought of using them to make number patterns. James took four matches and made the number $4$. Natalie added three more matches to create a design with two $4s$. They realized they could add $3$ matches each round to make one “extra four.” From this, they deduced that, in general, they needed $4+ 3(n-1)$ sticks to create a pattern with $n$ number $4$. Here $4+ 3(n-1)$ is called an algebraic expression.
\[5x+6\]
- $x$ is the variable whose value is unknown to us and can take on any value.
- $5$ is the coefficient of $x$ because it is a constant value used with the variable term and is well defined.
- $6$ is a constant-valued expression that has a specific value.
Types of Algebraic expressions:
There are three basic types of algebraic expressions.
- Monomial Algebraic Expression
- Binomial Algebraic Expression
- Polynomial Algebraic Expression
Monomial Algebraic Expression
An expression that has only one term is known as a monomial. Examples of monomial expressions include $4x^{4}$, $3xy$, $3x$, $8y$, etc.
Binomial Algebraic Expression
An expression is an algebraic expression that has two different terms. Examples of binomial numbers include $5xy + 8$, $xyz + x^{3}$, etc.
Polynomial Expression
In general, a polynomial is known as an expression with more than one term with non-negative integral exponents of the variable. Examples of polynomial expressions include $ax + by + ca$, $x^{3} + 2x + 3$, etc.
Expert Answer
The word more in the given phrase $4\: more\: than\:p$ shows plus. Therefore, the algebraic expression is
\[4+p\]
Numerical Result
The algebraic expression for the given phrase $4\:more\: than\:p$ is $4+p$.
Example
Write an algebraic expression for each word phrase. $3$ less than x
Solution
The word less in the given phrase $3\: less\: than\:x$ shows minus. Therefore, the algebraic expression is
\[3-x\]
The algebraic expression for the given phrase $3\:less\: than\:x$ is $3-x$.