Algebraic Expressions
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Constant
A symbol having a fixed numerical value is called a constant.

Variable
A symbol which takes various numerical values is called a variable.

Algebraic expression
An expression having one or more variables is called an algebraic expression.

An algebraic expression may or may not contain mathematical operators like the symbols of addition, subtraction and multiplication. The quantities in an algebraic expression - variable, constant or combinations of both, joined by plus or minus signs, are called its terms.

The elements whose product forms a term of an algebraic expression are called the factors of that term.  The numerical factor of a term containing a variable is called the coefficient of the term.

constants, variables, algebraic expression, expression, mathematical operator

constants, variables, algebraic expression, expression, mathematical operator

Monomials:
Algebraic expressions that contain only one term are called monomials.

          4x-1
          7x2
          10xyz

Binomials:
Algebraic expressions that contain only two terms are called binomials.

     7+3x
     2x½ + 3y2
     6x2 + 7y

Trinomials:
Algebraic expressions that contain only three terms are called trinomials.

      5 + 2x - 3y
      x + 2y2 - 9
      x2+y-2 - 2z2

Polynomials:
Algebraic expressions with all variables having whole number exponents or powers are called polynomials. The expressions in which the powers of variables are negative or rational numbers are not polynomials.

polynomial, not polynomials, fractional power, negative power, powers of variables negative, terms, like terms, unlike terms

Like terms:
Terms that have the same power of the same variable are called like terms.



Unlike terms:
Terms that do not contain the same power of the same variable are called unlike terms.

expression, subtraction of algebraic expressions, addition of algebraic expressions,

To add or subtract algebraic expressions
  1. Arrange the expressions in separate rows, so that all like terms are one below the other and all unlike terms are in separate columns.
  2. Write all terms with their correct positive or negative signs.
  3. While subtracting, keep in mind how the minus sign between the expressions changes the signs of the terms of the expression being subtracted.

Summary

Constant
A symbol having a fixed numerical value is called a constant.

Variable
A symbol which takes various numerical values is called a variable.

Algebraic expression
An expression having one or more variables is called an algebraic expression.

An algebraic expression may or may not contain mathematical operators like the symbols of addition, subtraction and multiplication. The quantities in an algebraic expression - variable, constant or combinations of both, joined by plus or minus signs, are called its terms.

The elements whose product forms a term of an algebraic expression are called the factors of that term.  The numerical factor of a term containing a variable is called the coefficient of the term.

constants, variables, algebraic expression, expression, mathematical operator

constants, variables, algebraic expression, expression, mathematical operator

Monomials:
Algebraic expressions that contain only one term are called monomials.

          4x-1
          7x2
          10xyz

Binomials:
Algebraic expressions that contain only two terms are called binomials.

     7+3x
     2x½ + 3y2
     6x2 + 7y

Trinomials:
Algebraic expressions that contain only three terms are called trinomials.

      5 + 2x - 3y
      x + 2y2 - 9
      x2+y-2 - 2z2

Polynomials:
Algebraic expressions with all variables having whole number exponents or powers are called polynomials. The expressions in which the powers of variables are negative or rational numbers are not polynomials.

polynomial, not polynomials, fractional power, negative power, powers of variables negative, terms, like terms, unlike terms

Like terms:
Terms that have the same power of the same variable are called like terms.



Unlike terms:
Terms that do not contain the same power of the same variable are called unlike terms.

expression, subtraction of algebraic expressions, addition of algebraic expressions,

To add or subtract algebraic expressions
  1. Arrange the expressions in separate rows, so that all like terms are one below the other and all unlike terms are in separate columns.
  2. Write all terms with their correct positive or negative signs.
  3. While subtracting, keep in mind how the minus sign between the expressions changes the signs of the terms of the expression being subtracted.

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