page_title: Polynomial expansion
section_title: Expansion of a polynomial written in factored form
hierarchical_section_title: Polynomial expansion / Expansion of a polynomial written in factored form
caption_attribution_description: English: An image showing the expansion of two equation multiplied together.
context_page_description: In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a sum of products. During the expansion, simplifications such as grouping of like terms or cancellations of terms may also be applied. Instead of multiplications, the expansion steps could also involve replacing powers of a sum of terms by the equivalent expression obtained from the binomial formula; this is a shortened form of what would happen if the power were treated as a repeated multiplication, and expanded repeatedly. It is customary to reintroduce powers in the final result when terms involve products of identical symbols.
  Simple examples of polynomial expansions are the well known rules
  when used from left to right. A more general single-step expansion will introduce all products of a term of one of the sums being multiplied with a term of the other:
context_section_description: To multiply two factors, each term of the first factor must be multiplied by each term of the other factor. If both factors are binomials, the FOIL rule can be used, which stands for "First Outer Inner Last," referring to the terms that are multiplied together.  For example, expanding
  yields
caption: Two expressions can be multiplied by using the commutative law, associative law and distributive law. (To multiply more than 2 expressions, just multiply 2 at a time)
exif: {}