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Factorising Algebraic Expressions

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notes

Factors of algebraic expressions:

  • When we factorise an expression, we write it as a product of factors. These factors may be numbers, algebraic variables, or algebraic expressions.

  • In algebraic expressions, we use the word ‘irreducible’ in place of ‘prime’.

  • An irreducible factor is a factor which cannot be expressed further as a product of factors.

  • 5 × x × y is the irreducible form of 5xy. Note 5 × (xy) is not an irreducible form of 5xy, since the factor xy can be further expressed as a product of x and y, i.e., xy = x × y.

Example

Factorise the following expressions and write them in the product form.
5t2.

5t2 = 5 × t2 = 5 × t × t.

Example

Factorise the following expression and write them in the product form.
6 ab2.

6 ab2 = 2 × 3 × a × b × b.

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