How to Simplify Expressions

Simplify Radical Expressions

Radical expressions are the combination of both variables and numbers inside a root. Radical expressions should be broken into pieces in order to get its simplest form.
Example: Simplify `1/sqrt(2)` +`1/8` = `1/sqrt(2)` +`1/(2sqrt(2))`
= `2/(2sqrt(2))` + `1/(2sqrt(2))`
=`3/(2sqrt(2))`

Simplify square roots

The process of obtaining the 'square root' of a number is termed as 'solving' or' simplification'. The number is broken down to its factors to obtain the number which satisfies the condition of being the square root of the number.
Example: Find `sqrt(48)` =`sqrt(2*2*2*2*3)` =`2*2sqrt(3)` =`sqrt(3)`
Fing `sqrt(x^(2)36)` =`sqrt(x*x*2*2*3*3)` =x*2*3 =6x

Simplify rational expressions

A rational expression is more than a fraction in which the numerator and/or the denominator are polynomials. Simplifying rational expression involve breaking down fractions.
Example:Solve `(x^(2)+3x+2)/(x+2)` = `(x^(2)+x+2x+2)/(x+2)` = `(x(x+1)+2(x+1))/(x+2)`
= `((x+1)(x+2))/(x+2)` =x+1

Simplify fraction

Simplify fraction involves breaking a bigger fraction to smaller one, converting mixed to improper fraction and then solving the problem.
Example: Solve 2`2/3` -`1/3` = `8/3` - `1/3` = `7/3`

Simplify exponents

Exponentiation is a mathematical operations, written as aⁿ, involving two numbers, the base a and the exponent n.
Example: Solve x².x³=x²⁺³=x⁵
Solve `x^(5)/x` =x⁵.x^-1=x^5-1=x⁴

Simplify algebraic expressions

An Algebraic Expression is a combination of numerals, variables and arithmetic operations such as +, -, * and /.
Example:Simplify 2x+5x-(4+5)x+7x-2
Solution: 2x+5x-(4+5)x+7x-2=2x+5x-9x+7x-2=14x-9x-2
=5x-2

Simplify complex fractions

If a fraction is composed of numerator and denominator as a fraction, it is called complex fractions.
Example:Solve `(3/4)/(6/8)` = `3/4` * `8/6` = `2/2` =1

Simplify equations

A number which satisfies the given equation is called a solution or root of that.‘Satisfying the equation’ means that if the variable (literal) involved in this is replaced by the number, then both sides of that become equal. Understand the basic concepts and master your subject.
Example:Solve 2x+3-6x=-7x
2x-6x+3=-7x
-4x+3=-7x
-4x+7x=-3
3x=-3
x=-1

Math Expressions

In this article we are going to discuss about math expressions concept . In algebra an expression may be used to designate a value, which value might depend on values assigned to variables occurring in the expression; the determination of this value depends on the semantics attached to the symbols of the expression. These semantic rules may declare that certain expressions do not designate any value; such expressions are said to have an undefined value, but they are well-formed expressions nonetheless.

Simplifying Math Expressions

In mathematical, expression is a finite group of algebraic terms and mathematical symbols combined with no equal or in equality sign. In algebra and in other branches of mathematics, letters are used to represent numbers with unknown or unassigned values.

A number represented by a wording is called a literal number, and any number expression in which one or more number symbols are letter is called a literal expression in algebra

Steps for simplify the math expressions :

Step 1: Group the terms containing the matching variable together in algebra expressions.

Step 2: Perform the operation in the parentheses for the variable and other.

Step 3: Rewrite the expressions and simplify the mathematical expressions.

Step 4: To check the equation, if there is able to simplify the expression, then repeat the step 1 to 4.

Basic natural law for mathematical expression:

In elementary algebra, we list the basic rules and properties of pre-algebra and give examples on they may be used natural law.

expect that a, b and c are variables or mathematical expressions using natural law.

1. Commutative Property of Addition In mathematical.

a + b = b + a 2. Commutative Property of Multiplication In mathematical.

a * b = b * a

3. Associative Property of Addition In mathematical.

(a + b) + c = a + (b + c)

4. Associative Property of Multiplication In mathematical.

(a * b) * c = a * (b * c)

5. Distributive Properties of Addition Over Multiplication.

a * (b + c) = a * b + a * c
and
(a + b) * c = a * c + b * c

Example : Solve 10x(2x+ x²)

Solution:

A(B+C)=AB+AC

Step 1: is to determine what terms represent A,B and C in the given equation.

A represents 10x.

B represents 2x.

C represents x²

Step 2: is to make the multiplication operation.

AB=10x(2x)=20x²

AC=10x(x²)=10x³

Step 3: is to rewrite the problem.

10x(2x+x²)=20x²+10x³

Source:tutorvista.com