SOLUTION: name and describe two types of Special Products that you may be able quickly recognize and factor if found embedded within a rational expression?

Question 535715: name and describe two types of Special Products that you may be able quickly recognize and factor if found embedded within a rational expression?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I would recognize the square of a binomial
and
a difference of squares

I would look for two monomials/terms that are perfect squares, such as
, ,
If there is only two such monomials, and they have opposite signs, then I would see it as a difference of squares.
If there were two such monomials, with the same sign, and a third term, I would figure out if the third term is double the product of the square roots of the other two.
For example, in
I recognize the perfect square terms , and .
Since they both appear with a minus sign (same sign), I would calculate the square roots (of the monomials without the minus sign, of course), as
, and .
Then I would calculate twice their product

Since it equals the third term, the factoring is

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