Question

Why do we use the distributive property when subtracting expressions?

Answer 1

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 we 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.

Answer 2

The 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.