Formulas & tables/Mathematics/Special products/Cube of a sum

Cube of a sum

(a+b)3=a3+3a2b+3ab2+b3(a+b)^3=a^3+3a^2b+3ab^2+b^3

Result unit: — (expression)

What it describes

The cube of the sum of two expressions.

Symbols

a,ba, b
arbitrary expressions (numbers)

Where it comes from

The expansion of the third power of a sum — four terms with coefficients 1, 3, 3, 1 (from Pascal's triangle).

When to use it

Expanding cubes of sums.

Example

Expand (x+1)3(x+1)^3.
Substitutiona=xa=x, b=1b=1.
Resultx3+3x2+3x+1x^3+3x^2+3x+1.

Related formulas

Square of a sum Binomial theorem

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