Learning the expressions is the same thing as learning your multiplication tables - it helps you to understand algebra. And algebra allows you to understand things like logic, statistics, and all sorts of calculations where you don't know enough numbers to do a straight addition or multiplication or subtraction or division.
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Algebraic expressions are terms that do not include an equality sign
Yes. That is the definition of an algebraic expression.
Only like terms can be subtracted or added in algebraic expressions.
Algebraic expressions are terms that do not include an equality sign
Yes.