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# Factorisation - Factorisation by Regrouping Terms

#### notes

Look at the expression 2xy + 2y + 3x + 3.
You will notice that the first two terms have common factors 2 and y and the last two terms have a common factor 3. But there is no single favtors common to all the terms.
Suppose  (2xy + 2y) in the factor form:
2xy + 2y = (2 × x × y) + (2 × y)
= (2 × y × x) + (2 × y × 1)
= (2y × x) + (2y × 1) = 2y (x + 1)
Similarly , 3x + 3 = (3 × x) + (3 × 1)
= 3 × (x + 1) = 3 ( x + 1)
Hence, 2xy + 2y + 3x + 3 = 2y (x + 1) + 3 (x +1)

We observe  that a common factors (x + 1) in both the terms on the right hand side.
Combining the two terms,
2xy + 2y + 3x + 3 = 2y (x + 1) + 3 (x + 1) = (x + 1) (2y + 3)
The expression 2xy + 2y + 3x + 3 is now in the form of a product of factors. Its factors are (x + 1) and (2y + 3). Note, these factors are irreducible.

In factorization by regrouping sometimes the terms of the given expression need to be arranged in suitable groups in such a way that all the groups have a common factor.
Method of factoring terms:
Step 1: Arrange the terms of the given expression in groups in such a way that all the groups have a common factor.
Step 2: Factorize each group.
Step 3: Take out the factor which is common to each group.

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Factorisation by regrouping terms [00:19:00]
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