# Algebra 1 Basics, Algebra Variable &Algebra Coefficient Definition

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   3x + 2,  the constant is  2.

No matter what happens the the value of 3x, 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   3x + 6y  =  8,

the  x  coefficient is  3,  and the  y  coefficient is  6.

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.

3x + 6y  =  8     has 3 terms.

4x + y     has 2 terms.

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

### Like Terms:

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

7x2   and   2x2  are like terms.

y3y   and   100y   are all like terms.

5x4   and   3x3   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.

3x + y     and     x4     are expressions.

3x + y = 6     and     x4 = 1     are equations.

### Functions and Equations:

Functions and equations are also similar but not quite identical.

x2 + 2x + 1 = 0   is a quadratic equation.

f(x) = x2 + 2x + 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 x value that is input.

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  3x2  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.

2xy + 5x   is an example of a binomial.

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

x2 + 8x4   is an example of a trinomial.

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