Factorize x2 + 2xy + y2 – 9

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.

The above expressions are represented with the help of unknown variables, constants, and coefficients. The combination of these three terms is termed as an expression. unlike the algebraic equation, It has no sides or ‘equals to’ sign.

Types of Algebraic expression

There are majorly three types of algebraic expressions based on the number of terms present in the algebraic expression. They are monomial expression, binomial expression, and polynomial expression. Let’s take a look at them,

Monomial Expression: An expression that has only one term is termed 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 that has more than one term with non-negative integral exponents of a variable is termed a polynomial expression. Examples of polynomial expression include ax + by + ca, x³ + 5x + 3, etc.

Some Other Types of Expression

Apart from monomial, binomial, and polynomial types of expressions which are numeric expressions and variable expressions. Let’s learn about them,

Numeric Expression: An expression that consists of only numbers and operations, but never includes any variable is termed a numeric expression. Some of the examples of numeric expressions are 14 + 5, 20 ÷ 2, etc.
Variable Expression: An expression that contains variables along with numbers and operations to define an expression is termed variable expression. Some examples of a variable expression include 4x + y, 4ab + 33, etc.

Some algebraic formulae

(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)

Factors of algebraic expression

Finding the factors of the given expression which refers to finding two or more expressions whose product is the given expression is termed as the factors of algebraic expression. The process of finding two or more expressions whose product is the given expression in terms is known as the factorization of algebraic expressions. Here, Factor is a term used to express a number as a product of any two numbers like x and y as xy. Here, x and y are the factors. It also refers to finding out the factors of the given algebraic expression.

For example: 3a²b + 5ab²

Here, 3a²b and 5ab² are the two terms.

3a²b = {3 × a × a × b}, these are the factors of the term.
5ab² = {5 × a × b × b}, these are the factors of the term.

When the factors are multiplied, they result in the original number or an expression that is factorized.

For example, consider the expression (3x²+ 9x). It can be factorized as 3x(x + 3). When multiplied (3x) and (x + 3), the original expression obtained as (3x²+ 9x).

Factorize x² + 2xy + y² – 9

Solution:

Given expression, x² + 2xy + y² – 9

By splitting,

= x² + 2xy + y² – 9

= (x + y)² – (3)² {x² + 2xy + y²= ( x + y )²}

Now use, x²– y² = (x + y)(x – y)

= (x + y + 3) (x + y – 3)

GeeksforGeeks

Factorize x2 + 2xy + y2 – 9

Types of Algebraic expression

Factors of algebraic expression

Factorize x² + 2xy + y² – 9

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