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Expression has no answer. a equation has an answer
Difference in math means subtraction. To express the difference between 6 and 2 you would use the equation 6 - 2 = 4.
an equation has an equals sign.
The second difference of a quadratic equation being one indicates the second derivative at that point is positive. What you do from there depends on what property or transformation you're looking for with respect to the equation.
An expression has no equal sign whereas an equation does have an equal sign