Question

Show two methods of factoring the expression ax - bx - ay + by. Is the result the same?

Answer 1

There are two ways to factor the given expression by grouping:

1. by grouping variables first:
ax-bx-ay+by=(ax-bx)-(ay-by)=x(a-b)-y(a-b)=(x-y)(a-b)

2. by grouping coefficients first:
ax-bx-ay+by=(ax-ay) - (bx-by) = a(x-y) -b(x-y) = (a-b)(x-y)

You'll have to decide if the results are the same.

Answer 2

Any factoring method will result in the same thing. If you get something different with one of them then it is not a proper factoring method.