Simplifying an expression means to rewrite it in a simpler form without changing its value. This is often done by combining like terms or using mathematical rules to reduce the number of terms in the expression.
In mathematics, identities are equations or expressions that are always true, regardless of the value of the variables involved. These can be used to simplify expressions and solve equations.
Some basic identity rules in algebra include the commutative property, associative property, and distributive property. The commutative property states that the order of the terms in an expression can be changed without changing its value. The associative property states that the grouping of terms in an expression can be changed without changing its value. The distributive property states that multiplying a number or variable by a sum or difference is the same as multiplying it by each term separately and then adding or subtracting the products.
An expression is fully simplified when it cannot be simplified any further using the basic rules of algebra. This means that all like terms have been combined, parentheses have been removed, and the terms are in their simplest form.
Some tips for simplifying expressions include identifying like terms, using the basic identity rules, and remembering the order of operations. It can also be helpful to work from the inside out, simplifying terms within parentheses first, and to double check your work by plugging in values for the variables to see if the original and simplified expressions have the same value.