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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 $3-x$.