an algebraic expression
yes.
Like terms.
They are identical or equivalent.
Expressions have to contain numbers and letters.
In algebra, expressions that have the same variable and exponents are considered like terms. For example, the terms (3x^2) and (5x^2) are like terms because they both contain the variable (x) raised to the same exponent of 2. Like terms can be combined through addition or subtraction, while terms with different variables or exponents cannot be combined in this way.
yes.
Two expressions are "equivalent" if they have the same result for any values of the variable or variables.
Terms that contain the same variable is called "like terms".
There is no specific name. They can be fractions which contain algebraic or trigonometric or non-integral exponential expressions.
Yes, (7ab) is like (ab) in that both expressions contain the same variables, (a) and (b). The difference is that (7ab) is scaled by a factor of 7, meaning it is seven times the value of (ab). In terms of algebraic expressions, they represent different quantities but share the same variable structure.
Like terms.
They are identical or equivalent.
Terms that contain the same variable is called "like terms".
Expressions have to contain numbers and letters.
In algebra, expressions that have the same variable and exponents are considered like terms. For example, the terms (3x^2) and (5x^2) are like terms because they both contain the variable (x) raised to the same exponent of 2. Like terms can be combined through addition or subtraction, while terms with different variables or exponents cannot be combined in this way.
In the same way that you would factorise any other expressions that do not contain an equality sign depending on the expressions of which none have been given.
Algebraic expressions may contain variables but they are not normally called variables. In fact, if they are related to identities, they need not be variable. For example, (4x2 + 8xy + 4y2)/(x + y)2 is an algebraic expression, but it is not a variable: it equals 4.