common factor in algebra

Common Factor in Algebra

Common factor is simply the "what is alike/same in every Algebraic term". Say, in 2x +2y, "2x" is a term and "2y" is also a term. What are the common color in 2x +2y expression? Red. What else are common aside from color alone? So it's  the number 2. When I remove the number "2" from the expressions, the remaining would be "x + y". So, "2" is the common factor of 2x +2y. I wanna put "2" outside of the "x + y" expressions, so it is found to be 2(x + y).  It's that simple. In the case of expression "2x +4y", it can be {2x + 2(2)y} as to factor "4y" into 2(2)y. So same color, same number
was put outside the group, and it is 2(x + 2y). In this page, we will do some basics.

Illustrative Examples

Factor out the common factor.

1). ax + ay = a (x + y)

2). 2a - 2b = 2 (a - b)

3). 2x + 4y = 2 x +2(2)y = 2(x + 2y)

4). 6a - 9b = 3(2) - 3(3)b = 3(2 - 3b)

5). 6a + 4b -2c = 2(3)a +2(2)b - 2c = 2(3a -2b -c)

Sample Problem

Factor out the common factor.

1). 2x + 4y = 2 (x +2y)

2). 3a - 6b = 3(a -2b)

3). 3x + 3ax = 3x(1+a)

4). 4a -6ab + 2ac = 2a(2 -3b +c)

5). 2x +4y -6z = 2(x +2y -3z)

QUIZ:

Factor out the common factor. Click the ____ for your answer, or click here for a video solution.

1). 3a + 6b =   ___________

2). 2a + 4b - 6c =  ___________

3). -2x -10y =   ___________

4). 3m - 6n + 3p =  ___________

5). 5x - 10xy + 5xz =  ___________

6). 7a + 21b + 14c =  ___________

7). -6 + 12ab =  ___________

8). 9a + 6ab - 3ac =  ___________

9). 2a + 2b - 2c =  ___________

10).  a + b + c =  ___________

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Related References: link 1, link 2

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