Binomials theory

POLYNOMIALS: Binomials

 

Binomials are polynomials consist 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.

Example:

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|01

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|02

 

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:

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|03

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|04

 

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

Example:

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|05

 

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

Example:

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|06

 

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

Example:

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|07

 

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

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

Example:

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|08

We remove the square of the common term:

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|09

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

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|10

The uncommon terms are multiplied:

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|11

So, finally, it will be:

bioprofe |exams with exercises about physics, chemistry and mathematics | Binomials

bioprofe |binomials theory|12

 

You can download the App BioProfe READER to practice this theory of Binomials and Polynomials with self-corrected exercises. It is available for Windows computers, Windows tablets, Android tablets and iPads

 

Books that we recommend to extend knowledge of the subject

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