Question

Why do we use the distributive property when subtracting expressions?

Answer 1

distributive properties of addition and
subtraction can be used to rewrite
expressions for a variety of purposes. In
each case, you are distributing the outside
multiplier to each number in the
parentheses, so that multiplication occurs
with each number before addition or
subtraction occurs.

Answer 2

Consider the example

(3x+5) - (x-10)

When we subtract off the (x-10), we are basically subtracting off x and also subtracting off -10. This is the same as adding on 10 because -(-10) = 10

So we would have these steps

(3x+5)-(x-10)

3x+5-x+10

2x+15

Often students forget to distribute the negative all the way through and would have 3x+5-x-10 as an incorrect step. You need to multiply that -1 through to each term, so that's why the distributive property is used.