Answer
An algebraic expression is the combination of variables and numbers connected with the algebraic operation.
Work Step by Step
An algebraic expression is the combination of variables and numbers connected with the algebraic operation (addition, subtraction multiplication, division and power or roots).
Examples:
(a) \[x+y+56\]
(b) \[{{y}^{2}}+5y+\sqrt{y}\]
An algebraic expression contains terms, coefficient, factors, like terms, constant etc.
Consider an example of an algebraic expression,
(1) \[9{{x}^{2}}+5y+2{{x}^{2}}+4\]
The terms of an algebraic are those parts that are connected by addition.
In the above algebraic expression \[9{{x}^{2}},5y,2{{x}^{2}},4\]are terms.
The numerical value that multiplied with the variable is called the coefficient.
In the above algebraic expression \[9,5,2\] are the coefficient of \[{{x}^{2}},y,{{x}^{2}}\] respectively.
Factor of an expression includes every variable, their product and the number that divide the expression completely.
In the above algebraic expression, the factor of the term \[9{{x}^{2}}\]are \[x,{{x}^{2}},9,9x,9{{x}^{2}}\].
Like terms are the expression that contain same variable and have same power.
In the above algebraic expression, \[9{{x}^{2}}\] and \[2{{x}^{2}}\]are the like terms.
