Factoring Difference of Squares
The main way to spot Difference of Squares is that there's no middle term. Once identified, you'll make quick work of gems like x2-16, x2 - 4, and y2-1.
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Hard Factoring Problems (free)
Don't let your teacher confuse you! In this video I encourage you to forget what you know about factoring and come at it with my tried-and-true "trial and error" method, which over the years has saved many of my students from factoring oblivion.
Easier Factoring Problems
Factoring problems can get rough, but in this video we'll just do ones where the x2 doesn't have a number in front of it. I also cover the sign rules.
Basic Factoring: "Factoring Stuff Out"
This video is about the first thing you learn in factoring: pulling out "like terms" or "the greatest common factor" (gcf). Basically, it's where you take an expression that doesn't have any parentheses, and you put parentheses in it.
In these videos we'll cover all forms of factoring polynomials, from "factoring stuff out" to quadratics to sum and difference of cubes. We'll also learn factoring by u-substitution & grouping.
Common Algebraic Canceling Mistakes
More fun with rational expressions! In this video I show you when you're allowed to cancel exponents and when you're not. We'll also get into the difference between "cross multiplying" and "cross canceling," though I can't explain why those two things have to have such similar names.
Negative Exponents
Negative exponents don't have to be confusing, they're just rational expressions in disguise. Just move that term to the denominator if it's in the numerator, the numerator if it's in the denominator, or reciprocal it if it's neither. That's not confusing at all, right?
Basic Exponent Rules & Rational Expressions
"Rational Expressions" is just algebra-speak for "fractions with variables in them". The rules involved with "like bases" are many: Adding exponents when we multiply. Subtracting them when we divide. Canceling and combing terms when we multiply and divide rational expressions.
Combining exponents, canceling terms, multiplying rational expressions and equations, multiplying and dividing variables with various exponents, negative exponents: if it's got an exponent, this chapter covers it.
Law of Cosines
In my tutoring experience, students have a much easier time with Law of Cosines problems because it's just plug-and-chug. No burn questions for this one!
The Law of Sines "Ambiguous Case"
If you haven't come across this in class yet, you pretty much need to watch the video to see why it's ambiguous. Suffice to say, they should have called it the "twice as much work" case!
Basic Law of Sines problems
There are two kinds of Law of Sines problems. "Easy" ones involve AAS and ASA, and non inverse trig functions. "Hard" refers to SSA, a.k.a. "The ambiguous case", the subject of the next video.
Laws of Sines & Cosines
Basic Law of Sines problems
The Law of Sines "Ambiguous Case"
Law of Cosines
Earlier in Trig, we've already had a few videos about solving right triangles for missing sides, so how is this chapter different? It no longer has to be a right triangle! These problems are way more complicated than SohCahToa, yet in this chapter students often seem relieved to actually be "doing something" again rather than learning "a bunch of stuff you'll never see again".
Graphing Tangent & Co-Tangent
Disco's back, baby! After seeing this video, you'll get a nice upper body workout during homework and tests as you mime "right-handed disco" and "left-handed disco", leaving your highly confused classmates eating your disco dust.
Graphing Secant & Co-Secant
Gone are the days of disco. No, unfortunately the only visual metaphor that seems to apply to graphs of secant and co-secant are U's and upside-down U's. Oh well.
I put these four in a separate chapter from Sine & Cosine for two reasons. First, many non-honors students don't even have to do these, so why scare you. Second, you should really get good at sine & cosine graphs first, since these four badboys are way easier if you base them on sine and cosine graphs, which is the approach I find helps students the most.
Vertical Shift in Sine & Cosine Graphs
Vertical shift is the number at the end of the equation in problems like f(x)=2sinX+4 and y=cosX-2. This is the second-most annoying way a trig teacher can make a problem harder, but if you follow my "simple five step plan for graphing sine and cosine!" you'll get through it okay.
Phase Shift (honors only) (free)
Phase shift is the horizontal shift that happens when there's a number in the parentheses with the X, as in y=sin(X-2). Sure, these problems are difficult and take forever, but if you follow my "simple six step plan for graphing sine and cosine!" you stand a chance.
Amplitude & Period
Every journey begins with the first step. This journey isn't great, and we're starting with two steps: amplitude and period, a.k.a. the numbers surrounding the sin or cos. Not too bad, especially if you use my patented "simple four step plan for graphing sine and cosine!"
Sine & Cosine Graphing Overview
In this video I introduce the terminology of amplitude, period, vertical shift and phase shift, but save actually learning to work with them for later videos. The main thing here is to get the broad idea, and see the similarities and differences between the graphs of sine and cosine.