The basic concept of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are termed here as variables. this expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is termed as a coefficient.
An idea of expressing numbers using letters or alphabets without specifying their actual values is termed an algebraic expression.
What is an Algebraic Expression?
In mathematics, It is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, etc.. these Expressions are made up of terms. Algebraic expressions are the equations when the operations such as addition, subtraction, multiplication, division, etc. are operated upon any variable.
A combination of terms by the operations such as addition, subtraction, multiplication, division, etc is termed as An algebraic expression (or) a variable expression.
Examples
2x + 4y – 7, 3x – 10, etc.
These above expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three as terms is termed as an expression. unlike the algebraic equation, It has no sides or ‘equal to’ sign.
Some of its examples include
- 2x + 2y – 5
- 4x – 20
- 4x + 7
We can say that 4x + 7 is an example of an algebraic expression and here 4x + 7 is a term
- x is a variable whose value is unknown and which can take any value.
- 4 is known as the coefficient of x, as it’s a constant value used with the variable term.
- 7 is the constant value term that has a definite value.
Types of Algebraic expression
- Monomial Expression
- Binomial Expression
- Polynomial Expression
Monomial Expression
An expression which has only one term is termed as a Monomial expression .
Examples of monomial expressions include 4x4, 2xy, 2x, 8y, etc.
Binomial Expression
An algebraic expression which is having two terms and unlike are termed as a binomial expression
Examples of binomial include 4xy + 8, xyz + x2, etc.
Polynomial Expression
An expression which has more than one term with non-negative integral exponents of a variable is termed as a polynomial expression.
Examples of polynomial expression include ax + by + ca, x3 + 5x + 3, etc.
Some Other Types of Expression
We have other expressions also Apart from monomial, binomial, and polynomial types of expressions which are
- Numeric Expression
- Variable Expression
Numeric Expression
An expression which consists of only numbers and operations, but never include any variable is termed as numeric expression.
Some of the examples of numeric expressions are 11 + 5, 14 ÷ 2, etc.
Variable Expression
An expression which contains variables along with numbers and operation to define an expression is termed as A variable expression.
Some examples of a variable expression include 5x + y, 4ab + 33, etc.
Some algebraic formulas
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2
(x + a)(x + b) = x2 + x(a + b) + ab
(a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – b3 – 3ab(a – b)
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
There are some terms of algebraic expression which are basically used
Examples of using these terms
If 2x2+3xy+4x+7 is an algebraic expression.
Then, 2x2, 3xy, 4x, and 7 are the Terms
- Coefficient of Term: 2 is the coefficient of x2
- Constant Term: 7
- Variables: here x, y are variables
- Factors of a Term: If 2xy is a term, then its factors are 2, x and y.
- Like and Unlike Terms: Example of like and unlike terms:
- Like Terms: 4x and 3x
- Unlike Terms: 2x and 4y
Solve (6 – 3w)(-w2)
Solution:
(6 – 3w)(-w2)
By simplifying
= (6 – 3w)(-w2)
= [6 × (-w2)] – [3w × -(w2)]
= -6w2 – (-3w3)
= -6w2 + 3w3
= 3w2 (-2 + w)
= 3w2 (w – 2)
Similar Questions
Question 1: Simplify: 7 – 3(x – 1).
Solution:
here we have
7 – 3(x – 1)
= 7 – 3x + 3
= 10 – 3x
= -3x + 10
Question 2: Simplify 5x2 + 7x – 9 = 4x2 + x – 18
Solution:
5x2 + 7x -9 = 4x2 + x – 18
5x2 + 7x -9 – 4x2 – x + 18 = 0
x2 +6x + 9 = 0
(x + 3)2 = 0 {(a + b)2 = a2 + 2ab + b2}