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Factoring: Special Cases Part I - Concept
Adding and subtracting rational expressions is similar to adding fractions. When adding and subtracting rational expressions, we find a common denominator and then add the numerators. To find a common denominator, factor each first. This strategy is especially important when the denominators are trinomials.
Alright guys let's be straight, factoring is a real drag I get it like I'm a Math teacher I do the stuff all day long. Factoring can be a real drag cause it's so much guess and check that's why you want to have any shortcuts or any strategies you can that will make it be more easy, some things you can look for are what we're going to talk about today, special cases.
If you see trinomials that look like these first two guys, they're what we call "perfect square trinomials" because their factored form looks like a binomial squared. That guy is a+b squared and this guy is a-b squared. Notice the only difference in the trinomial is the plus or minus sign there same thing here the only difference is the plus or minus sign. Again those are called "perfect square trinomials." So if you're given something like this and asked to factor it or if you see the words "perfect square trinomial" think about this definition right here. This right here this third one is called "difference of perfect squares," difference meaning it is subtraction problem, the way you factor it looks like this one plus sign and one minus sign it doesn't matter which order you put them in as long as one's positive and one is negative the core thing is if you were to FOIL this guy out your positive ab and negative ab terms would be eliminated because it additive inverses and your result is just a squared take away b squared.
So you don't have to memorize these, these are just tricks but if you do memorize them, they might help you with some of factoring problems. I know factoring is hard but I promise you these kinds of tricks or formulas will help you when you get into your homework.