## Binomials theory

**POLINOMIALS**

A **binomial** is a polynomial consists of two monomials separated by a plus (+) or a minus (-) sign.

Binomials operations are:

1.- **Binomial squared:** is equal to the square of the first term, more or less, double product of the first by the second one plus the square of the second term.

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2.- **Binomial cube:** is equal to the cube of the first term, more or less, three times the square of the first by the second one, plus the triple of the first by the square of the second one, more or less the cube of the second term.

__Example:__

3.- **Difference of**** squares:** it is equal to a sum by difference.

__Example:__

4.- **Sum of cubes:** we decompose the cube in a binomial squared multiplied by a sum of the two terms.

__Example:__

5.- **Difference of cubes:** It is decomposed in a binomial difference squared multiplied by a subtraction of both simple terms.

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6.- **Product of two binomials with a common term:** it is possible to do it by multiplying polynomials or by the following rule:

- Firstly the square of the common term is removed.
- We do the sum of the terms that are not common and then they are multiplied by the common term.
- We multiply the uncommon terms.

__Example:__

We remove the square of the common term:

The subtraction of terms which are not common multiplied by the common term:

The uncommon terms are multiplied:

So, finally, it will be: