Factor Completely

Question

5xy + 25x - 3y - 15

 

Factor Completely

Can you factor this out??

Answer 1

The pattern will be easier to recognize if you rearrange the terms.

 

5xy - 3y + 25x - 15

 

you should be able is discern a 5x - 3 pattern

 

(5x - 3)y + (5x - 3)5

 

which can be rearranged using the Distributive Law.

 

(5x - 3)(y + 5)

 

 

Answer 2

To factor this equation, you need to do F-O-I-L (First-Outside-Inside-Last) in reverse.

 

Here is F-O-I-L:

   (ax+b)(cy+d)  =   acxy + adx + bcy + bd

                                F         O       I       L

 

Here is the problem:

                               5xy  + 25x - 3y  - 15

 

So,

    ac = 5  

    ad = 25

    bc = -3

    bd = -15

 

Now, notice that the 4 terms can be factored in pairs:

  5xy + 25x  - 3y  - 15

  5x(y + 5) - 3(y + 5)

   (5x -3)(y + 5)               [Distributive Property in reverse]