To start things off in Algebra, and in Algebra 1 basics, it’s helpful to learn the definition of certain words that are commonly used.

This page will explain exactly what is meant by some of the most common language in Algebra.

### Variables:

Variables are usually letters of the alphabet, for example ** a , b , x , y**.

As the name variable would imply, the value these letters have can vary.

A variable in Algebra can be given any value or set of values, where such values aren’t initially specified.

With the expression

**+**

*x***4**, the variable is

**.**

*x*### Definition of a Constant:

A constant is fixed and does not change value in an algebraic expression.

For example in **3 x** +

**2**, the constant is

**2**.

No matter what happens the the value of 3

*x*, 2 remains the same.

### Algebra Coefficient Definition:

For an Algebra coefficient definition, coefficients can sit beside variables and are often a number, though a coefficient can be a letter or symbol also in some cases.

A coefficient multiplies the variable it sits alongside, though the sign for multiplication is not present.

A coefficient of value 1, is also left unwritten, and we just have the variable itself.

In **3 x** +

**6**=

*y***8**,

the

*coefficient is 3, and the*

**x***coefficient is 6.*

**y**A coefficient of a variable could also be a fraction, for example we can have something like \bf{\frac{1}{2}}

*.*

**x**### Terms in Algebra:

A term in Algebra is an individual part of an expression/equation.

**3 x** +

**6**=

*y***8**has 3 terms.

**4**+

*x***has 2 terms.**

*y***7**is 1 term, the coefficient is 7 and there are two variables in the term, though a term could have even more variables.

*xy*### Like Terms:

‘Like terms’ are terms that have the exact same variable part or parts as each other.

**7 x**

^{2}and

**2**

*x*^{2}are like terms.

**,**

*y***3**and

*y***100**are all like terms.

*y***5**

*x*^{4}and

**3**

*x*^{3}are NOT like terms, as the variable has a different power in each term.

It’s also worth noting that you can only carry out addition and subtraction when the terms are like in Algebra.

### Expressions and Equations:

Expressions and equations in Algebra 1 basics are similar, but not quite the same thing.

An algebraic expression is a combination of numbers and variables with operations signs.

Where as an equation is comprised of two expressions that are connected by an equals sign.

**3 x** +

**and**

*y***−**

*x***4**are expressions.

**3**+

*x***=**

*y***6**and

**−**

*x***4**=

**1**are equations.

### Functions and Equations:

Functions and equations are also similar but not quite identical.

For example with a quadratic.

*x*^{2} + **2 x** +

**1**=

**0**is a quadratic equation.

**=**

*f(x)*

*x*^{2}+

**2**+

*x***1**is a quadratic function.

The equation has a specific value or values that will solve it, while the function produces a value depending on the specific

**value that is input.**

*x*A more detailed and involved explanation of this difference can be read at the

*jdmeducational.com*website.

### Monomial, Binomial, Trinomial:

Expressions in Algebra and Math can have specific names to describe how many terms are in the expression.

A monomial is an expression which contains only one term, such as **3 x**

^{2}or

**.**

*y*Even just a single number is a monomial.

A binomial is an expression where there are two terms present, which are not like terms.

**2**+

*xy***5**is an example of a binomial.

*x*A trinomial is an expression containing three terms, which again are not like terms.

*x*^{2}+

**8**−

*x***4**is an example of a trinomial.

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