If the math equation you're doing has letters or other symbols that stand for numbers, you're likely doing algebra. You probably took your first algebra class early in your high school years.
The noun algebra comes from Arabic word al jebr, meaning "reunion of broken parts," which appeared in the title of mathematician alKhwarizmi's famous book on equations. In algebra you use basic arithmetic like addition and subtraction, but the quantities you're working with are often unknown — that's why they're represented by letters. You might remember solving algebra equations that look like this: a(b + c) = ab + ac. The letters a, b, and c all represent a number.
Definitions of algebra
1
n the mathematics of generalized arithmetical operations
 Types:
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quadratics
a branch of algebra dealing with quadratic equations

linear algebra
the part of algebra that deals with the theory of linear equations and linear transformation

vector algebra
the part of algebra that deals with the theory of vectors and vector spaces

matrix algebra
the part of algebra that deals with the theory of matrices

decomposition, vector decomposition
the analysis of a vector field
 Type of:

pure mathematics
the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness