1. Algebra is a branch of mathematics dealing with symbols and the rules for manipulating these symbols. 2. The fundamental concept is to solve equations where variables represent unknown values. 3. For example, in the equation $x + 3 = 7$, we solve for $x$ by isolating it: $x = 7 - 3$. 4. This simplifies to $x = 4$, which is the solution. 5. Algebra also includes working with expressions, such as expanding $(x + 2)(x - 3)$. 6. Expand by applying distributive property: $x(x - 3) + 2(x - 3) = x^2 - 3x + 2x - 6$. 7. Combine like terms to get $x^2 - x - 6$. 8. Another key part is factoring, which is the reverse of expanding; for instance, factor $x^2 - x - 6$. 9. Find two numbers that multiply to $-6$ and add to $-1$: these are $-3$ and $2$. 10. So, $x^2 - x - 6 = (x - 3)(x + 2)$. 11. Algebra is powerful for solving real-world problems involving unknown quantities by setting up and solving equations.