Why Do Negative Exponents Switch Locations?
Negative exponents are often taught as a rule to memorize: move the base across the fraction bar and make the exponent positive. But why does that work? In this lesson, we use exponent patterns and the quotient rule to discover where negative exponents come from. By comparing exponent subtraction with expanded multiplication, you’ll see that […]
Why is there a ± for quadratics?
Why do we write ± when solving quadratic equations, but not when evaluating square roots? In this lesson, we’ll explore one of the most common misconceptions in algebra and uncover the reasoning behind it. You’ll learn how functions, inverses, and solving equations are connected, and why: ✔️ √25 = 5 ✔️ x² = 25 has […]
Rules of Exponents Explained
Exponent rules don’t have to be a collection of formulas to memorize. Once you understand the patterns behind exponents, the rules begin to make sense and become much easier to use. In this video, you’ll learn the most important exponent rules used throughout Algebra, Geometry, College Algebra, and ACT Math. We’ll work through examples and […]
Simplifying Square Roots Using Perfect Squares
Simplifying radicals doesn’t have to be complicated. The key is learning how to identify perfect square factors hidden inside the radical and use them to rewrite the expression in simplest form. In this video, you’ll learn a step-by-step method for simplifying square roots by breaking numbers into factors, finding the largest perfect square, and pulling […]
Matrix Multiplication Made Easy | Row by Column
Matrix multiplication can seem confusing at first, but once you understand the row-by-column process, everything starts to make sense. In this video, you’ll learn how to multiply matrices step-by-step by matching rows from the first matrix with columns from the second matrix. We’ll work through examples together and break down exactly where each entry in […]
Synthetic Division: Faster Than Long Division
Synthetic division is one of the fastest ways to divide polynomials—and it’s much easier than traditional polynomial long division once you understand the process. In this video, you’ll learn how synthetic division works step-by-step, including how to set up the problem, what the numbers represent, and how the multiplication-and-addition pattern helps you find the quotient […]
Domain and Range Explained | Inputs and Outputs
What do the linear function and the absolute value function have in common? More importantly, how are their domains and ranges different? In this video, we’ll introduce the concepts of domain and range by comparing two familiar functions: a linear function and an absolute value function. You’ll learn how domain represents the possible inputs (x-values) […]
How to Find Intervals of Increase and Decrease
How can you tell if a function is increasing or decreasing? In this video, I show you a simple way to find intervals of increase and decrease by reading a graph from left to right. Instead of memorizing rules, you’ll learn how to recognize whether a function is moving upward or downward as the x-values […]
Squaring a Binomial: Why There’s a Middle Term
Why doesn’t (a+b)²+bx+c equal a²+b² ? In this video, I explain where the middle term comes from when squaring a binomial and why so many students make this common mistake. Instead of just memorizing a formula, you’ll see the logic behind the expansion and understand why the result includes the 2ab term. You’ll learn: • […]
Why Does Anything to the Zero Power Equal 1?
Have you ever wondered why anything raised to the zero power equals 1? Many students memorize the rule x^0 = 1, but few understand where it comes from. In this video, we’ll discover the pattern behind exponents and see why the zero exponent rule isn’t something you have to memorize—it actually makes perfect mathematical sense. […]