Simplify an Expression
Pre-AlgebraSimplifying an expression means rewriting it in its most compact form by combining like terms, applying properties, and removing unnecessary operations.
Definition
Simplifying an expression means combining everything you can so the expression is as short as possible, without changing its value.
Example
Simplify $3x + 5 + 2x - 1$. Combine the $x$ terms: $3x + 2x = 5x$. Combine the constants: $5 - 1 = 4$. Result: $5x + 4$.
Key Insight
A simplified expression is easier to evaluate and work with. Think of it as tidying up a messy room so it is easier to navigate.
Definition
To simplify an algebraic expression, apply the distributive property to remove parentheses, then collect and combine all like terms. The result should have no redundant operations and each variable term should appear only once.
Example
Simplify $2(3x - 4) + 5x$. Distribute: $6x - 8 + 5x$. Combine like terms: $(6x + 5x) - 8 = 11x - 8$.
Key Insight
Simplification is not solving. After simplifying, the expression still contains variables. Solving would require an equation (with an equals sign) and a specific value for the variable.
Definition
Simplification is the process of applying algebraic identities and rewrite rules to produce a canonical or reduced form of an expression. In computer algebra systems, canonical simplification relies on normal forms such as the expanded polynomial form or the rational canonical form. The concept of "simplest form" depends on context: factored form can be simpler than expanded form for some purposes.
Example
Simplifying $(x^2-9)/(x-3)$ involves factoring the numerator: $(x+3)(x-3)/(x-3) = x + 3$, with the restriction $x \neq 3$. Whether the factored or expanded form is "simpler" depends on the task.
Key Insight
No single universal definition of "simplest" exists in algebra. Computer algebra systems use specific normal forms and heuristics, which is why different systems can produce different-looking but equivalent results.