Expand your tools for solving systems of linear equations by exploring the method of solving by elimination. This technique allows you to eliminate one variable by performing addition, subtraction, or multiplication on both sides of an equation, allowing a straightforward solution for the remaining variable.

The square root approach to solving quadratic equations works not just for perfect squares, such as 3 × 3 = 9, but also for values that don't seem to involve squares at all. Probe the idea behind this technique, and also venture into the strange world of complex numbers.

Using graph paper and pencil, begin your exploration of the coordinate plane, also known as the Cartesian plane. Learn how to plot points in the four quadrants of the plane, how to choose a scale for labeling the x and y axes, and how to graph a linear equation.

Practice solving systems of two linear equations by graphing the corresponding lines and looking for the intersection point. Discover that there are three possible outcomes: no solution, infinitely many solutions, and exactly one solution.

Professor Sellers explains the topics covered in the series, the importance of algebra, and how you can get the most out of these episodes. Then, launch into the fundamentals of algebra by reviewing the order of operations and trying your hand at several problems.

Continue your study of math fundamentals by exploring various procedures for converting between percents, decimals, and fractions. Professor Sellers notes that it helps to see these procedures as ways of presenting the same information in different forms.

Discover that by following basic rules on how to treat coefficients and exponents, you can reduce very complicated algebraic expressions to much simpler ones. You start by using the commutative property of multiplication to rearrange the terms of an expression, making combining them relatively easy.

Deepen your insight into polynomial functions by graphing them to see how they differ from non-polynomials. Then learn how the general shape of the graph can be predicted from the highest exponent of the polynomial, known as its degree. Finally, explore how other terms in the function also affect the graph.

In some circumstances, quadratic expressions are given in a special form that allows them to be factored quickly. Focus on two such forms: perfect square trinomials and differences of two squares. Learning to recognize these cases makes factoring easy.

Combine rational functions using addition, subtraction, multiplication, division, and composition. The trick is to start each problem by putting the expressions in factored form, which makes the calculations go more smoothly. Leaving the answer in factored form also allows other operations, such as graphing, to be easily performed.