An expression is in simplest form when it has been rewritten to its clearest, most reduced representation under the rules being used: like terms are combined, common factors are removed, fractions are in lowest terms, and any special requirements for radicals or denominators have been met. When deciding which expression is in simplest form, look for an answer that is equivalent to the original expression but contains no unnecessary operations, factors, or complexity.
Quick note before moving on Worth keeping that in mind..
Introduction to Simplest Form
In mathematics, simplest form means that an expression has been changed without altering its value. The goal is to remove details that do not help represent the expression. Here's one way to look at it: the fraction (\frac{8}{12}) is equivalent to (\frac{2}{3}), but (\frac{2}{3}) is simpler because the numerator and denominator share no common factor greater than 1.
The same idea applies to algebraic expressions. The expression (4x+6x) can be simplified to (10x), and the fraction (\frac{15x}{25}) can be reduced to (\frac{3x}{5}). On the flip side, “simplest form” is not always completely universal. In practice, a polynomial may be considered simplified when it is expanded, such as (2x+6), while another context may prefer its factored form, (2(x+3)). Because of this, the correct interpretation depends on the type of expression and the mathematical convention being applied.
What Makes an Expression Simple?
An expression is generally close to simplest form when it follows these principles:
- Like terms are combined. Expressions such as (3x+5x) become (8x).
- Common factors are removed. The fraction (\frac{18}{24}) becomes (\frac{3}{4}).
- Numerators and denominators share no common factor. A rational expression should have no nonzero common algebraic factor unless domain restrictions are being preserved.
- Parentheses are removed when expansion is expected. As an example, (3(x+4))
