Introduction:

In mathematics, an algebraic expression is a finite combination of symbols that are well-formed according to the rules applicable in the context at hand. Symbols can designate values (constants), variables, operations, relations, or can constitute punctuation or other syntactic entities. The use of expressions can range from simple arithmetic operations. Let us see about algebraic expression mean and examples. (Source: Wikipedia)

Properties Algebraic expression mean:

Commutative property of algebraic expression

Addition: a + b="b" + a

For example: x2 +x= x + x 2

(2) 2 + 2 = 2+ (2) 2 (if we consider x="2)

4+2=2+4

6="6

Multiplication: (if a="5" ,b=3)

For example: a * b = b*a

5*3 = 3*5

15 = 15

The Distributive property of algebraic expression

Addition: a * (b + c) = a * b + a * c

Multiplication: (a + b) * c = a * c + b * c

Associative property of algebraic expression

Addition: (a + b)+ c = a + (b + c)

Multiplication: (a * b) * c = a * (b * c)

The reciprocal of a is `1/a` : a *`(1/a)` = 1

The additive inverse of a is –a: a + (-a) = 0

Example problems for algebraic expression mean:

Example 1: Check that the following expression is satisfy the Commutative property of algebraic expression: x2 +x= x + x 2.

Solution:

(2) 2+2=2 + (2) 2 (if we consider x="2)

4+2=2+4

6="6

Therefore the given expression has the commutative property of addition.

Example 2: Solve the expression: |-4x + 4| + 5 = 5

Solution:

Given |-2x + 2| + 5 = 5

|-2x + 2| = 0 (subtract 5 on both sides)

- 2x + 2 = 0

-2x =-2

x = 1

Example 3: Solve for n: 11m – 11n = 5

Solution:

Given 11m – 11n = 5

-11n = 5 – 11m (subtract 11m on both sides)

- n = `(5 -11m) / 11` (divide 11 on both sides)

n = m - `5/11` (multiply by - sign on both sides)

In this section we have seen about the basic concepts and meaning of algebraic expression.