Factoring Algebraic Expressions

Any term is formed as a product of factors. For example, in the term 14ab 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 3x + 6

Write each term as a product of irreducible factors:

3x = 3 × x

6 = 2 × 3

3x + 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, 3x + 6 = 3(x + 2), where 3 and (x + 2) are the factors of 3x + 6, and these factors are cannot be reduced further.

Example: Factorise 10xy + 20x

10xy = 2 × 5 × x × y

20x = 2 × 2 × 5 × x

10xy + 20x = (2 × 5 × x × y) + (2 × 2 × 5 × x)

The above two terms have 2 × 5 × x = 10x as the common factor.

By distributive property, 10x × (y + 2) = (2 × 5 × x × y) + (2 × 2 × 5 × x)

So, 10xy + 20x = 10x(y + 2), where 10x and (y + 2) are the factors of 10xy + 20x, and these factors cannot be reduced further.

Check Point

1. Factorise 7xy + 49x
2. Factorise 12x + 36
3. Factorise mn + 10m
4. Factorise 24a + 30
5. Factorise 11x + 121xy

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