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Algebraic expressions are expressions consisting of one or more numbers, variables and the product of these along with one or more arithmetic operations.

Variable is a letter which is a literal symbol and it may taken any value of number either positive or negative, whole number or fraction or complex number.

Usually variable is denoted by a small letter English Alphabet. For example, x,a,b,y,z,t etc

The four arithmetic operations used are

- Addition, a+b
- Subtraction, a-b
- Multiplication, a.b
- Division, a/b for any numbers or variables a and b

Parenthesis are given first preference in the expression and the terms inside it treated as single term.

Terms are the parts of algebraic expression that are connected by addition and subtraction.

Factors are the parts of algebraic expressions that are connected by multiplication.

Coefficient of a term is a factor or group of factors of the term by which the remainder of the term is to be multiplied.

If no numerical in front of literal factor, it is considered to be of coefficient 1.

Examples: xy, coefficient is 1

a, coefficient is 1 etc

Note:

When there are several number of operations in the expression, use the PEMDAS property to evaluate the order of operations

**P:** Evaluate Parenthesis

**E:** Evaluate Exponent

**M:** Evaluate Multiplication

**D:** Evaluate Division

**A:** Evaluate Addition

**S:** Evaluate Subtraction

**Monomial:** If an algebraic expression conatins only one term then it is called monomial.

Examples: 3x,4y,7xy etc

3 is the coefficient of x

4 is the coefficient of y

7 is the coefficient of xy

7x is the coefficient of y

Binomial: If an algebraic expression contains two terms then it is called binomial.

Examples: 3x+4y, a+b, y+4z, 9y-z etc

Trinomial: If an algebraic expression contains three terms, then it is called trinomial.

Examples: x-y+z, 3-y+z,

$x^2+x+1$ which has a special name quadratic expression

Polynomial: An algebraic expression containing more than one number of terms is called polynomial. Also, all the binomials, and trinomials are polynomials.

Examples: x+10y, $7x^2+5x+11$, 5x+y-z+11 etc.

**Types of Terms:**

There are two types of terms Like terms and Unlike terms

Like terms are the terms containing literal factors in which same variables raised to same power

Unlike terms are the terms which do not contain same variables

**Combining Terms:**

Like terms can be combined to a single term by adding or subtracting the coefficients of terms and placing the result infront of the literal factor or variable

Examples: 6x+10x=(6+10)x = 16x , $7x^2+4x^2=(7+4)x^2=11x^2$, $5x^3-3x^3=(5-3)x^3=2x^3$

Unlike terms cannot be combined to single term

$2x^3+5x^2$, $3x^5+4y^3-2x^2+11x-2$