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Identifying quadratic expressions

Unless you are sure whether an expression is quadratic or not, you will not be able to apply an appropriate method to solve it. Further, sometimes it may prove difficult to identify whether an algebraic expression is quadratic or not. This post is written to help you identify whether an algebraic expression is a valid quadratic expression or not.

Basic Steps of Identifying Quadratic Expressions:
  • Simplify the expression (opposite of factoring)
  • Find the greatest exponent on a variable in the expression
  • If the greatest exponent is 2 it is a quadratic expression
You may need to apply different mathematical procedures to simplify the expression to its simplest form. This is the opposite of factoring, which involves writing the given expression as a product of two or more terms. In simplifying the expression, remember that no products should be left unmultiplied. The following examples will guide you on how to simplify an expression.

The following expressions may not appear to be quadratic expressions at the first glance:
  • x(x + 3)
  • (x3 + 2x) / 3x
  • (y3x3 + x2y2) / xy
But, on simplifying each of the above expressions, we obtain the following expressions:
  • x2 + 3x
  • x2/3 + 2/3
  • y2x2 + xy
Each of the above expressions are quadratic because the greatest exponent in each expression is 2.

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