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Factorisation by regrouping terms

Last updated at March 16, 2023 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

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.