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Math Easy Tutorials

Follow along as I explore the amazing capabilities of mathematics!
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two different types of complex functions are shown in the text above it, and below them is
Quadratic Formula
Calculus
Math Resources
Easy Tutorial
Two By Two
Science
How To Apply
Maths Resources
Cubic Formula Proof Step 2: Applying Vieta's Substitution to Obtain a Quadratic Equation
In this video I go over the second step in deriving the Cubic Formula, and this involves converting our earlier PQ version of the cubic formula into a quadratic formula using Vieta's substitution.
the first solution is to write an x and y formula
Raising Boys
Cubic Formula Proof Step 3: First Solution of y
In this video I go over the third step of the Cubic Formula proof which involves plugging our z value back into Vieta's substitution to obtain our first y solution.
an image with the word cauchy - schwarzer inequaility written on it
Absolute Value
Quiz Questions
True False
The Dot
Quick Saves
True-False Quiz Questions 22: Cauchy–Schwarz Inequality
In this video I show that the absolute value of the dot product has a maximum value of the lengths of each vector multiplied by each other. This relation is known as the Cauchy-Schwarz Inequality.
an image of the formula for two different functions, with one being given as x and y
Substitution Method
First Step
The First
Cubic Formula Proof Step 1: Removing x^2 term via PQ Substitution
In this video I go over the first step in deriving the Cubic Formula, which is to eliminate the x^2 term from the Cubic Equation by using the PQ Substitution method. This allows us to later apply Vieta's substitution to obtain a quadratic formula, which we can solve.
an image with the formulas for two different functions, and one that is written as 2
Cube Root
Cubic Formula Proof Step 4: Other Solutions of y using the Cube Root of Unity
In this video I go over the fourth step of the Cubic Formula proof which involves obtaining the complex solutions of y by considering the cube root of unity. Since the cube root of the z values from Vieta's substitution has 3 factors, we need to multiply the principle solution by the factors to obtain each separate solution.
the formula for quadtracing and substition method is shown in this diagram
Completing The Square
Educational Videos
Quadratic Formula by the PQ Substitution Method
In this video I solve the quadratic formula again, but this time using the PQ method instead of the complete the squares method that I used earlier. This is because the PQ method is utilized throughout the cubic formula proof, so this is a good preview.
the formula for cubic formula is shown in black and white, with an extra - large
Cubic Formula Proof
In this video I go over a complete derivation of the cubic formula, which is the solution to the cubic equation.
In this video I go over a quick intro to sequences (which are ordered lists of numbers) and series (which are sums of sequences). Isaac Newton represented functions as sums of infinite series, which paved the way for many applications in physics, chemistry, and science in general.
3:31
Introduction to Infinite Sequences and Series
In this video I go over a quick intro to sequences (which are ordered lists of numbers) and series (which are sums of sequences). Isaac Newton represented functions as sums of infinite series, which paved the way for many applications in physics, chemistry, and science in general.
In this video I go over a quick intro to sequences (which are ordered lists of numbers) and series (which are sums of sequences). Isaac Newton represented functions as sums of infinite series, which paved the way for many applications in physics, chemistry, and science in general.
Introduction to Infinite Sequences and Series
In this video I go over a quick intro to sequences (which are ordered lists of numbers) and series (which are sums of sequences). Isaac Newton represented functions as sums of infinite series, which paved the way for many applications in physics, chemistry, and science in general.
an image with the formulas for two different functions and one is written on it
Cubic Formula Proof Step 5: Putting it All Together to Solve for x
In this video I go over the fifth and final step of the Cubic Formula proof which involves putting all of the previous steps together to solve for the 3 solutions of x. Because I used the copy and paste method in Microsoft OneNote, I may be the first person to show the complete solution being derived in real-time!
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Math geometry
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Physics and mathematics
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the diagram shows two different ways to solve an problem with one solution, and another
Square Roots
Square
Square Root of Unity, Cube Root of Unity, and Complex Rotations
In this video I demonstrate that the square root of 1 (or unity) has two solutions while the cube root of unity has three solutions, two of which are rotations in the complex plane. I show this by first determining the factors using the difference of squares and cubes formulas.
This may contain: two different types of complex functions are shown in the text above it, and below them is
11:09
Cubic Formula Proof Step 2: Applying Vieta's Substitution to Obtain a Quadratic Equation
In this video I go over the second step in deriving the Cubic Formula, and this involves converting our earlier PQ version of the cubic formula into a quadratic formula using Vieta's substitution.
This may contain: the formula for quadtracing and substitution method is shown in black
6:43
Quadratic Formula by the PQ Substitution Method
In this video I solve the quadratic formula again, but this time using the PQ method instead of the complete the squares method that I used earlier. This is because the PQ method is utilized throughout the cubic formula proof, so this is a good preview.
the quadtracing formula for quadtracting and completing square roots with two equal squares
The Square
Quadratic Formula by Completing the Square
In this video I solve the quadratic equation by completing the square to obtain the famous quadratic formula.
This may contain: an image with the word cauchy - schwarzer inequaility written on it
2:28
True-False Quiz Questions 22: Cauchy–Schwarz Inequality
In this video I show that the absolute value of the dot product has a maximum value of the lengths of each vector multiplied by each other. This relation is known as the Cauchy-Schwarz Inequality.