Parallel (operator): Difference between revisions

Revision as of 21:41, 31 January 2023

Revision as of 22:49, 31 January 2023

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Using the distributive property twice, the product of two parallel binomials can be expanded as

:<math>\begin{align}

:<math>(a \parallel b) (c \parallel d) = ac \parallel ad \parallel bc \parallel bd.</math>

(a \parallel b) (c \parallel d)

&= a(c \parallel d) \parallel b(c \parallel d) \\[3mu]

:<math>(a \parallel b) (c \parallel d) &= ac \parallel ad \parallel bc \parallel bd.</math>

\end{align}</math>

The square of a binomial is

:<math>\begin{align}

:<math>(a \parallel b)^2 = a^2 \parallel ab \parallel ba \parallel b^2 = a^2 \parallel \tfrac12ab \parallel b^2.</math>

(a \parallel b)^2

:<math>(a \parallel b)^2 &= a^2 \parallel ab \parallel ba \parallel b^2 = a^2 \parallel \tfrac12ab \parallel b^2.</math>[3mu]

&= a^2 \parallel \tfrac12ab \parallel b^2.

\end{align}</math>

The cube of a binomial is