How to factor ax-ay-bx+by?

i know im supposed to group ax and ay, and then bx + by but im getting confused on teh signs. can you plz explain how to know which sign to keep when grouping and factoring a question like this

_ Page 1

Instead, group the x's and y's together to get:

ax - ay - bx + by = (ax - bx) + (-ay + by).

Factoring out the GCFs from the pairs of terms (x from the first and -y from the second):

(ax - bx) + (-ay + by) = x(a - b) - y(a - b).

Factoring out a - b yields (x - y)(a - b). Therefore:

ax - ay - bx + by = (x - y)(a - b).

I hope this helps!

#1

a(x-y) - b(x-y)

#2

(x - y)*(a - b)

#3

a(x-y)+b(y-x)

or x(a-b)+y(b-a)

#4

a(x-y)-b(x-y)

#5

you should see that when you need a + in the brackets then you should use - and - to make them positive...

#6

ax-ay-bx+by = (ax - bx) - (ay - by) = x(a - b) - y(a - b) = (a - b)(x - y)

#7

ax - ay is easily factored as a(x - y)

group the "b" terms as: ax - ay + (-bx + by) then swap the signs: ax - ay - (bx - by)

Now you have a(x - y) - b(x - y)

Then finally: (a - b)(x - y).

#8