Expressions and Equations
Expressions and Equations
In expressions and equations, an expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression or is any mathematical statement that consists of numbers, variables, and an arithmetic operation between them.
For example, 6m + 2 is an expression where 6m and 2 are the terms and m is the variable of the given expression separated by the arithmetic sign +.
Steps
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- True for all value X
- Common key terms
simplify
expand
Factorise
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- Example
4x+10y-5x-2
How to Simplify Algebraic Expressions?
The purpose of simplifying the algebraic expression is to find the simplified term of the given expression and to factorize or simplify the expression, we first know how to combine the like terms, factor a number, order of operations. In combining like terms, the variables having the same degree are gathered together and the constant terms are separated for the simplification process.
Expression Example
A few examples of expressions are as follows:
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- 2x + 5y – 3
- 2x – 1
- 3x +2 y
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Types of Expression
Arithmetic Expression
The expressions consist of number and arithmetic operators
Example: 45+67-8
Fractional Expression
The Expression consists of a fractional number and arithmetic operators
Example: 45/5 + 65/5
Algebraic Expression
The expression consists of unknown variables, numbers, and arithmetic operator.
Example: 6x+4
Equation
An equation is made up of two expressions connected by an equal sign the equation is an expression where two sides are connected through an equal sign (=). 2x + 1 = 9 is an equation, where 2x+1 is the left-hand side (LHS) and 9 is the expression’s right-hand side (RHS). The equal sign between LHS and RHS shows that the value of LHS is equal to the RHS of the expression.
How to Solve Algebraic Equations?
An algebraic equation contains two algebraic expressions separated by an equal sign (=) in between and the primary purpose of solving algebraic equations is to find the unknown variable in the given expression. While solving the equation, separate the variable terms on one side and constant terms on another side and the variable term can be isolated using the various arithmetic operations such as addition, subtraction, multiplication, division, and finding square roots, etc.
Equation Examples
Few examples of equations are:
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- 8m+5=10n
- a+4b = 12c+3
Types of Expression
Linear Equation
The standard form of linear equation with variables x and y is:
ax+by=c
Example : Linear equation with one variable : 20x – 60 = 0
Linear equations with two variables : 6x + 2y – 82 = 0
Quadratic Equation
Example : 5x2 – 5y -35=0
Here a = 5, b = -5 and c = -35
Cubic Equation
The standard form of cubic equation with variable x is:
ax3 + bx2 + cx + d = 0