# Factoring using grouping

Factoring using grouping is one method of separating out equations that have the same or common things in them. Things that can be factorized are letters or numbers.

In other words any common factors that can be found in the terms are taken out. The remainder is left inside the bracket.

Example 1

Factorize: 2x+xy

Solution: x is common in both terms, so we can take that out to give x(2+y)

Example 2

Factorize: 4a+2ab

Solution: 2 and a is common in both terms, so we can take that out to give 2a(2+b)

Example 3

Factorize: -6p²q+3p

Solution: 3 and p is common in both terms, so we can take that out to give 3p(-2p+1)

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Example 4

Factorize: 5x + 10y + bx + 2by

Solution: There is no common factor in all the terms, but only in some with each other. It is clear that 5 is a common factor in the first 2 terms and b is a common factor in the last 2 terms.

So this expression can be expressed in the following way

(5x+10y)+(bx+2by)

5(x+2y)+b(x+2y)

Now we can see that (x+2y) is common factor in both terms so can be taken out.

So: 5(x+2y)+b(x+2y)=(x+2y)(5+b)

The final solution to 5x + 10y + bx + 2by=(x+2y)(5+b)

Example 5

Here is a question asked by a tweeter 6wy-xz-2xy+3wz

The solution can be viewed here, you need a twitter account to view it.

One way to check answers to factoring by grouping is to multiply out the brackets. If it gives the original answer then the factorization is correct.

This type of factorization is called grouping 'two by two' and usually consists of four terms.

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