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Algebraic Expressions

  • Algebraic expressions are formed by combining variables with constants using operations of addition, subtraction, multiplication and division.

For example: 4xy, 2x2 – 3, 7xy + 2x, etc.

In an algebraic expression, say 2xy – 3x2 + 2; 2xy, (–3x2), 2 are known as the terms of the expression.

The expression 2xy – 3x2 +2 is formed by adding the terms 2xy, (–3x2) and 2 where 2, x, y are factors of the term 2xy; (–3), x, x are factors of the term (–3x2); 2 is the factor of the term 2.

For an expression, the terms and its factors can be represented easily and elegantly by a tree diagram.

Tree diagram for the expression 2xy – 3x2 +2:

Note: In an expression, 1 is not taken as separate factor.  

  • The numerical factor of a term is known as its coefficient. For example, for the term –3x2y, the coefficient is (–3).
  • The terms having the same alg…

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