As an algebra tutor, I will cover a wide range of topics, including:

1. Basic Algebraic Operations: Teaching students fundamental operations like addition, subtraction, multiplication, and division with algebraic expressions.

2. Solving Equations: Helping students solve linear equations, quadratic equations, and systems of equations.

3. Inequalities: Explaining how to work with and solve linear and quadratic inequalities.

4. Polynomials: Covering polynomial operations, factoring, and long division.
Functions: Introducing the concept of functions, domain, range, and graphing linear and quadratic functions.

5. Exponents and Radicals: Teaching the rules of exponents, simplifying radicals, and working with rational exponents.

6. Quadratic Equations: In-depth exploration of quadratic equations, including the quadratic formula and completing the square.

7. Linear Algebra: Introducing matrix operations, determinants, and solving systems of linear equations using matrices.
Rational Expressions: Simplifying and solving equations involving rational expressions.
Word Problems: Helping students translate real-world problems into algebraic equations and solve them.

8. Algebraic Word Problems: Teaching strategies to solve word problems using algebraic techniques.

9. Polynomials and Factoring: Covering polynomial long division, synthetic division, and factoring techniques.

10. Absolute Value Equations and Inequalities: Solving equations and inequalities involving absolute value expressions.

11. Functions and Graphs: Teaching students how to graph various functions, including linear, quadratic, and absolute value functions.

12. Exponential and Logarithmic Functions: Introducing exponential and logarithmic functions and their properties.

13. Conic Sections: Discussing the properties of conic sections, including circles, ellipses, hyperbolas, and parabolas.

14. Complex Numbers: Explaining the concept of complex numbers, operations with complex numbers, and solving equations involving them.

15. Advanced Topics: Depending on the student's level, we can explore advanced algebraic topics like sequences and series, permutations and combinations, and more.

Lessons will be tailored to your students' specific needs and abilities.