If x+y=r and x-y=s, in terms of x and y, what is r^2-s^2? Please show step by step. Thanks.

Let’s do this two ways. First, with substitution. If r=x+y and s=x-y, then we can rewrite r^2-s^2 as (x+y)^2-(x-y)^2. Then we can simplify that:


The other way to go is to plug in. Say x=3 and y=2. That makes r=5 and s=1. Now you’re looking for r^2-s^2=5^2-1^1=24. Which answer choice gives you 24 when you plug in x=3 and y=2? 4xy does: 4(3)(2)=24.

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