# Factoring Algebraic Expressions

## Grade 7 Math Worksheets

Any term is formed as a product of factors. For example, in the term 14*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.

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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 a 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*)

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