Q: Who invented algebraic expressions?

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Algebraic expressions are terms that do not include an equality sign

Only like terms can be subtracted or added in algebraic expressions.

Yes. That is the definition of an algebraic expression.

Algebraic expressions are terms that do not include an equality sign

Algebraic expressions are terms that do not include an equality sign

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no algebraic expressions do not have equal signs but equations do.

Algebraic expressions are terms that do not include an equality sign

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.

Only like terms can be subtracted or added in algebraic expressions.

the word algebraic is arabic.

Yes. That is the definition of an algebraic expression.

Algebraic expressions are terms that do not include an equality sign

Algebraic expressions are terms that do not include an equality sign

An expression with a variable.

Yes.

Algebraic expressions allow you to organize the information so you can make a easier decision

An expression consists of algebraic terms and has no equality sign