How to factor 8(x-y) + a(y-x)

[medellinheel]

How to factor 8(x - y) + a(y - x)

The answers are as follows

a. (8+a)(y-x)
b. (8-a)(y-x)
c. (a-8)(y-x)
d. (a-8)(x-y)

The book says c is the correct answer but doesnt really explain how it came to that answer. Can someone explain this to me?

 

[srmichael]

The answers are as follows

a. (8+a)(y-x)
b. (8-a)(y-x)
c. (a-8)(y-x)
d. (a-8)(x-y)

The book says c is the correct answer but doesnt really explain how it came to that answer. Can someone explain this to me?

You can rewrite (x-y) as -(y-x). Do that and see if you get C.

 

[fcabanski]

You can also plug in some values for a, y and x. Eliminate the answer equations with results that don't match the original equation's result. If more than one answer remains, plug in new values for a, y and x, until you eliminate all but one choice.