# Factoring Algebraic Expressions

Home | Online Math Tutoring | 7th Grade Math Tutoring | **Factoring Algebraic Expressions**

*ab*is formed by the factors, 2, 7,

*a*and b. Similarly, we can factorise an algebraic expression and express it as a product of factors. These factors may be numbers, algebraic expressions or variables. Factoring is the process of writing a polynomial as the product of two or more polynomials.

*Example:*Factorise 3

*x*+ 6

##### Write each term as a product of irreducible factors:

3*x*= 3 ×

*x*6 = 2 × 3 3

*x*+ 6 = (3 ×

*x*) + (2 × 3) The above two terms have 3 as the common factor. By distributive property, 3 × (

*x*+ 2) = (3 ×

*x*) + (2 × 3) So, 3

*x*+ 6 = 3(

*x*+ 2), where 3 and (

*x*+ 2) are the factors of 3

*x*+ 6, and these factors are cannot be reduced further.

*Example:*Factorise 10

*xy*+ 20

*x*10

*xy*= 2 × 5 ×

*x*×

*y*20

*x*= 2 × 2 × 5 ×

*x*10

*xy*+ 20

*x*= (2 × 5 ×

*x*×

*y*) + (2 × 2 × 5 ×

*x*) The above two terms have 2 × 5 ×

*x*= 10

*x*as the common factor. By distributive property, 10

*x*× (

*y*+ 2) = (2 × 5 ×

*x*×

*y*) + (2 × 2 × 5 ×

*x*) So, 10

*xy*+ 20

*x*= 10

*x*(

*y*+ 2), where 10

*x*and (

*y*+ 2) are the factors of 10

*xy*+ 20

*x*, and these factors cannot be reduced further.

#### Check Point

- Factorise 7
*xy*+ 49*x* - Factorise 12
*x*+ 36 - Factorise
*mn*+ 10*m* - Factorise 24
*a*+ 30 - Factorise 11
*x*+ 121*xy*

##### Answer key

- 7
*x*(*y*+ 7) - 12(
*x*+ 3) *m*(*n*+ 10)- 6(4
*a*+ 5) - 11
*x*(1 + 11*y*)

*Download/Solve a **Worksheet** for Factoring Algebraic Expressions *

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