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?

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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) About Me  (Show Source):
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I would recognize the square of a binomial
a%5E2%2B2ab%2Bb%5E2=%28a%2Bb%29%5E2 and
a difference of squares
a%5E2-b%5E2=%28a%2Bb%29%28a-b%29
I would look for two monomials/terms that are perfect squares, such as
4, 81x%5E2, 16x%5E4y%5E6
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 36x-81x%5E2-4
I recognize the perfect square terms 4, and 81x%5E2.
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
2, and 9x.
Then I would calculate twice their product
2%282%29%289x%29=36x
Since it equals the third term, the factoring is
36x-81x%5E2-4=%28-1%29%2881x%5E2-36x%2B4%29=%28-1%29%289x-2%29%5E2