# Collect

Collect[expr,x]

collects together terms involving the same powers of objects matching x.

Collect[expr,{x1,x2,}]

successively collects together terms that involve the same powers of objects matching x1, then x2, .

Collect[expr,var,h]

applies h to the expression that forms the coefficient of each term obtained.

# Details and Options • Collect[expr,x] effectively writes expr as a polynomial in x or a fractional power of x.
• Collect[expr,x,Simplify] can be used to simplify each coefficient separately.
• Collect automatically threads over lists in expr, as well as equations, inequalities and logic functions.

# Examples

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## Basic Examples(4)

Combine like terms involving :

Collect terms involving :

Collect terms involving :

Collect each power of :

Simplify each coefficient:

## Scope(6)

### Basic Uses(3)

A polynomial:

A Puiseux polynomial:

Collect with respect to first, then collect with respect to :

Collect with respect to a pattern:

Collect derivative terms:

Factor each coefficient after collection of terms:

Collect terms over the integers modulo :

## Options(1)

### Modulus(1)

Collect over the integers modulo 2:

## Applications(1)

When a polynomial has many variables, it can be put into many different forms. Here is a polynomial in three variables:

Collect reorganizes the polynomial so that is the dominant variable:

If is specified as the parameter, the terms are organized with as the leading variable:

When two variables are specified, the function will collect with respect to first, then collect with respect to :

Or collect with respect to first, then collect with respect to :

## Properties & Relations(2)

Expand is effectively the inverse of Collect:

The order of variables matters: