Binomial formulas

Calculation of the three binomial formulas. The binomial formulas are used to multiply out products with two different variables.

To perform the calculation enter the values of the two variables, then click the 'Calculate' button.

Binomial formulas

The binomial formulas are formulas used in algebra for transforming products from binomials. Binomials refer to mathematical expressions with two terms that are connected by addition or subtraction.

The binomial formulas are used as mnemonic formulas, which are intended to make it easier to multiply expressions in brackets and prevent calculation errors. They allow the factorization of terms, i.e. the transformation of certain sums and differences into products.

First binomial formula:

\( ( a + b )^2 = a^2 + 2ab + b^2\)

Derivation:

\(( a + b )^2 = ( a + b ) * ( a + b ) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2\)

Second binomial formula:

\( ( a - b )^2 = a^2 - 2ab + b^2\)

Derivation:

\( ( a - b )^2 = ( a - b ) * ( a - b ) = a^2 - ab - ba + b^2 = a^2 - 2ab + b^2\)

Third binomial formula:

\( ( a + b ) * ( a - b ) = a^2 - b^2\)

Derivation:

\(( a + b ) * ( a - b ) = a^2 - ab + ba - b^2 = a^2 - b^2\)