Factor by grouping:

Question

Factor by grouping: 12ax + 5by + 4bx + 15ay.

Answer 1

12ax + 5by + 4bx + 15ay

Since 4 is a factor of 12 and 5 is a factor of 15 group those terms together:

12ax + 4bx + 5by + 15ay

4x(3a + b) + 5y(b + 3a)

4x(3a + b) + 5y(3a + b)

(3a + b)(4x + 5y)

Answer 2

The first two terms have no factors in common. Likewise, the last two terms have no factors in common. So it will work out more easily if we re-arrange the equation a bit to group terms that have common factors:

12ax + 4bx + 15ay + 5by

Now factor the common factors out of the first two terms and the second two terms:

4x(3a+b) + 5y(3a + b)

Now factor out the (3a + b):

(3a + b)(4x + 5y)