College algebra help!!!

Question

Express as a polynomial. (Simplify your answer completely.)

(√x +√y)(√x-√y)

Answer 1

Since you indicated “college math,” I will mention that there are such things called “design patters” and you will use these when you learn to do substitution in more complicated expressions.

The specific “pattern” being taught here is:  (a+b)(a-b) = a^2 – b^2       (remember this!)

           Use FOIL to show this.

 

The substitution is:       a = √x

                                  b = √y

 

So,   a^2 = x

        b^2 = y

 

The answer to the problem (soon, you will immediately recognize) is (x-y).

Answer 2

(√x+√y)(√x-√y)=√x√x-√y√y=x-y  (√y√x-√y√x=0)

the final answer is x-y