When I read " We work out this example as if it were 3(x - y) - 5(2y - x). We begin by multiplying out using the distributive property"

 

Does "multiplying out using the distributive property" just mean multiplying everything inside the bracket by what's outside it, in this case 3 & 5?

Pretty much yes.

 

It means the x AND the -y both get multiplyed by the 3 (the factor 3 is distributed through each term in the brackets) and the 2y and the - x get multiplied by the 5 (the factor 5 is distributed through that set of brackets).

 

 

Therefore it expands to: 3x - 3y -10y + 5x (care with the PLUS 5x.... - x -)

To further clarify, the problem is more like 3 (x + -y) + -5 (2y + -x). You must distribute the -5 therefore making the last term -(-5x) = +5x.

Knowing that the distributive property is there, so that 'multiplying out' is a valid operation is important:

1. For the sake of rigour
2. Because sometimes the distributive property doesn't hold.