Factoring Algebraic Expressions

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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 the 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
Answer key
  1. 7x(y + 7)
  2. 12(x + 3)
  3. m(n + 10)
  4. 6(4a + 5)
  5. 11x(1 + 11y)

Download/Solve a Worksheet for Factoring Algebraic Expressions 

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