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Simplify

▪ Simplify[ expr ] performs a sequence of algebraic transformations on expr, and returns the simplest form it finds.
▪ Simplify tries expanding, factoring and doing other transformations on expressions, keeping track of the simplest form obtained.
▪ The following options can be given:

▪ FullSimplify does more extensive simplification than Simplify.
▪ See the Mathematica book: Section 1.4.4Section 3.3.9.
▪ See also: FullSimplify, Factor, Expand, TrigExpand, PowerExpand, ComplexExpand.


Further Examples

Simplify returns these polynomials in factored form.

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This variation shows that Simplify may not factor completely.

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And here Simplify does nothing at all. This behavior, at first glance inconsistent, is explained by the default notion of simplicity used by the program, which is largely based on the expression's LeafCount.

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The leaf count is not the only consideration, however. Here, Log[256] is considered simpler than 4 Log[4], but Log[10000] is not simpler than 4 Log[10]. You can override this behavior; see the Further Examples for ComplexityFunction.

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This integral returns a sum of three terms.

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Differentiating the result gives an expression that is more complicated than the original integrand, but mathematically equivalent to it.

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Simplify gets back to the original form of the expression.

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See also the examples for ComplexityFunction and FullSimplify.