They both use PEMDAS or Order of Operation
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Numerical expressions solely include numbers, while algebraic expressions may contain a variable like x. An example of a numerical expression is 1+2 and an example of an algebraic expression is 2x+3y=0.
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.
An expression consists of algebraic terms and has no equality sign
The numerical factor of a term is called the "coefficient."
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