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Equations are made from expressions.
These are two expressions, not equations. Expressions do not have solutions, only equations do. NB equations include the equals sign.
a rational function.
Both have a value
Equations don't have multiples. Fortunately, those are expressions, not equations. Depending on the values of 'x' and 'y', the least common multiple of 4x2y5 and 6x3y2 could be less than 12x3y5, but it's not more.
expressions don't have an equal sign and equations do
Equations are made from expressions.
In the same way that you would solve equations because equivalent expressions are in effect equations
They can but don't have to.
no algebraic expressions do not have equal signs but equations do.
These are two expressions, not equations. Expressions do not have solutions, only equations do. NB equations include the equals sign.
It may be possible to solve equations. Expressions cannot be solved until they are converted, with additional information, into equations or inequalities which may have solutions.
They both have numbers and symbols
a rational function.
Both have a value
Equations don't have multiples. Fortunately, those are expressions, not equations. Depending on the values of 'x' and 'y', the least common multiple of 4x2y5 and 6x3y2 could be less than 12x3y5, but it's not more.
Algebraic expressions are the written relations of or between variables. For example, x2, 1/x, and x + y + z are all algebraic expressions. Algebraic equations are simply algebraic expressions that equate to something. For example, x2 = 4, 1/x = y, and x + y + z = 42 are all algebraic equations. In general, one differentiates algebraic expressions from exponential, trigonometric, hyperbolic, and logarithmic expressions by requiring algebraic expressions to be confined to polynomial expressions. I've added a link regarding polynomials below.