Indicated operations and simplify

Question

(√a+√b)(√a-√b)

Answer 1

This problem can be solved quickly if you use the following formula:

 

(x+y)(x-y) = x² - y²

 

It is a good idea to memorize the above formula.

 

So, for the given problem: (√a+√b)(√a-√b) = (√a)²-(√b)² = a-b (Answer)

Answer 2

Lola,

These factors are essentially the same as a difference of squares problem, but you need to employ the standard FOIL method of multiplying factors.  The FOIL method is simply (First, Outside, Inside, Last)

 

Now you have the factors:

(√a + √b)(√a - √b)

And you need to put it into full form.

√a√a(F)  - √a√b(O)  + √a√b(I)  - √b√b(L)

Combine like terms and simplify:

a + 0 + b

a - b

Answer 3

(√a+√b)(√a-√b)

 

Apply the distributive property:

 

√a√a - √a√b + √b√a - √b√b = a - b