Factorisation by regrouping terms

Last updated at April 16, 2024 by

Suppose we want to factorise,

  2 x y + 3 x + 2y + 3

 

We note that,

   2xy & 2y both have 2

And

  3x & 3 both have 3

 

So, we put them together

 

  (2xy + 2y) + (3𝑥 + 3)

2.jpg

 

So,

  2𝑥y + 3𝑥 + 2y + 3 = (𝑥 + 1) (2y + 3)

 

Factorise 4ab − 5a − 12b + 15

Factorisation by regrouping terms - Part 2

Transcript

(2𝑥y + 2y) + (3𝑥 + 3) Both have 2 & y as common factor Both have 2 & y as common factor = 2y (𝑥 + 1) + 3 (𝑥 + 1) Now, (𝑥 + 1) is common between them both = (𝑥 + 1) (2y + 3) So, 2𝑥y + 3𝑥 + 2y + 3 = (𝑥 + 1) (2y + 3) Factorise 4ab − 5a + 12b + 15 4ab − 5a + 12b + 15 = (4ab − 12b) + (15 − 5a) Both have 4 & b as common factor Both have 3 as common factor = 4b (a − 3) + 5 (3 − a) Writing (3 − a) = −(a − 3) = 4b (a − 3) − 5 (a − 3) Taking (a − 3) common = (a − 3) (4b − 5)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.