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Definition of «algebra»

The term "algebra" has its roots in the Arabic word "al-jabr," which means "completion" or "restitution." It was first used by the mathematician al-Khwarizmi, who wrote a book called "Al-Jabr wa'l-Muqabilah" (Translation: "The Composition of Algebra and Balancing"). In this book, al-Khwarizmi introduced the concept of solving linear equations using symbols to represent unknowns.

Over time, the term "algebra" came to be used more broadly to refer to a branch of mathematics that deals with the study of relationships between variables, including algebraic expressions and equations, polynomials, matrices, and functions. In essence, algebra is concerned with finding patterns and expressing them in mathematical terms, using symbols and formulas to represent and solve problems involving those patterns.

Usage examples

  1. Solving equations: In algebra, we use variables and symbols to represent unknown values in equations. For example, x + 5 = 10 is an algebraic equation where we can use algebraic methods to find the value of the variable x.
  2. Simplifying expressions: Algebra allows us to simplify complex mathematical expressions by combining like terms and using the properties of arithmetic. For instance, in the expression 3x + 2x - 5x, we can use algebraic techniques to simplify it to 0x or simply 0.
  3. Solving word problems: Algebra is crucial in solving real-world problems by translating verbal descriptions into mathematical expressions and equations. For example, if a word problem states "Jennifer is twice as old as her brother, and their combined ages are 30," we can use algebraic equations like j = 2b and j + b = 30 to find their ages.
  4. Factoring polynomials: Algebra involves factoring polynomials into their simplified or prime form. For instance, the expression x^2 - 4 can be factored as (x - 2)(x + 2) using algebraic methods like the difference of squares.
  5. Quadratic equations: Algebra allows us to solve quadratic equations using methods like factoring, completing the square, or the quadratic formula. For instance, x^2 + 4x - 5 = 0 is a quadratic equation that we can solve algebraically to find the values of x.

Phrases with «algebra»

Sentences with «algebra»

  • This paper examines the effects of policies that increase the number of students who take the first course in algebra in 8th grade, rather than waiting until 9th grade. (caldercenter.org)
  • I have incorporated the use of algebra in this lesson to stretch and challenge students. (tes.com)
  • The lesson then has a separate differentiated section for algebra in shape in which they must form and solve equations. (tes.com)
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See also

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