Page 141 - MarceAlgebra Demystified

128 CHAPTER 6 Factoring

Factoring by Grouping

Sometimes you can combine two or more terms at a time in such a way that
each term has an algebraic expression as a common factor.

Examples

3
2
3x 3 þ x x
If 3 is factored from the first two terms and x is factored from the last
2
two terms, we would have two terms with a factor of x 1.
2 3 2 2 2
3x 3 þ x x ¼ 3ðx 1Þþ xðx 1Þ¼ð3 þ xÞðx 1Þ
You could also combine the first and third terms and the second and
fourth terms.
2 3 2 3 2
3x 3 þ x x ¼ 3x þ x 3 x ¼ x ð3 þ xÞ ð3 þ xÞ
2
¼ðx 1Þð3 þ xÞ
2
3xy 2y þ 3x 2x ¼ yð3x 2Þþ xð3x 2Þ¼ðy þ xÞð3x 2Þ

2 2 2 2 2
5x 25 x y þ 5y ¼ 5ðx 5Þ yðx 5Þ¼ð5 yÞðx 5Þ
4 3 3 3
4x þ x 4x 1 ¼ x ð4x þ 1Þ ð4x þ 1Þ¼ðx 1Þð4x þ 1Þ

Practice

2
1: 6xy þ 4xy þ 9xy þ 6x ¼
3 2
2: x þ x x 1 ¼

3: 15xy þ 5x þ 6y þ 2 ¼

4 3
4: 2x 6x x y þ 3y ¼
3 2
5: 9x þ 18x x 2 ¼