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# Do all algebraic expressions have to have variables for example would 3 plus 4 equals 9 be an expression or would it need to be n plus 4 equals 9 to be an expression?

3 + 4 = 9 is not an expression, it is an equation (which happens to be false).

An equation without a variable is simply a statement which is either true (a tautology) or false. It's main use is probably at the end of a proof where you may show that the left hand side of some equation is numerically the same as the right hand side which proves your proposition.

n + 4 = 9 is also not an expression, but an equation. An equation with a variable can divide the domain into distinct partitions such that the equation is true if the value of the variable is within those partitions and not if they are outside. This may enable you to derive further information about he variable(s). Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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