Factor by Grouping

Factor by Grouping

Factor by grouping when a polynomial has four terms, or when terms can be split into groups that reveal a common factor. The goal is to rewrite the expression as a product of simpler factors.

1) Group the terms

Usually, pair the first two terms and the last two terms:

• (ax + ay + bx + by)
• ( (ax + ay) + (bx + by) )

If needed, rearrange the terms so the groups share a factor.

2) Factor each group

Take out the greatest common factor from each pair:

• ( ax + ay = a(x+y) )
• ( bx + by = b(x+y) )

Now the expression looks like two parts with the same binomial factor.

3) Factor the common binomial

When both groups contain the same factor, pull it out:

• ( a(x+y) + b(x+y) = (x+y)(a+b) )

4) Check your result

Multiply the factors back out to make sure you get the original polynomial. If the expansion matches, the factoring is correct.

Helpful tip

If you do not see a common factor after grouping, try a different arrangement of the terms. The right grouping should create the same binomial in both parts.

Always simplify the final answer as completely as possible.