#### 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.