Determine if the Expression is a Perfect Square -24xy^2

Problem

−24*x*y2

Solution

1. Identify the requirements for a term to be a perfect square. A perfect square expression must be the result of squaring another expression, meaning it must have a positive coefficient and all variables must have even exponents.

2. Check the sign of the coefficient. The coefficient is −24 Since it is negative, the expression cannot be a perfect square of a real expression because the square of any real number is non-negative.

3. Check the exponents of the variables. The variable x has an exponent of 1 which is odd. A perfect square must have even exponents for all variables.

4. Conclude that the expression fails multiple criteria for being a perfect square.

Final Answer

−24*x*y2* is not a perfect square.

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