Question 1067827
.
{{{a^3 + b^3 + 3a^2b + 3ab^2}}} = {{{(a + b)^3}}}.



It is &nbsp;<U>ONE OF THE BASIC</U>&nbsp; short multiplication formula of Algebra.


In my school years it was required to know it at the day and at the night as the multiplication table or the alphabet.



1. The <B>cube of the sum formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{(a + b)^3 = a^3 + 3a^2*b + 3a*b^2 + b^3}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The-cube-of-a-sum-formula.lesson>The cube of the sum formula</A> 



2. The <B>cube of the difference formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;{{{(a - b)^3 = a^3 - 3a^2*b + 3a*b^2 - b^3}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The-cube-of-a-difference.lesson>The cube of the difference formula</A> 



3. The <B>sum of cubes formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{a^3 + b^3 = (a + b)*(a^2 - ab + b^2)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The-sum-of-cubes-formula.lesson>The sum of cubes formula</A> 


4. The <B>difference of cubes formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{a^3 - b^3 = (a - b)*(a^2 + ab + b^2)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The-difference-of-cubes-formula.lesson>The difference of cubes formula</A> 




Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Shortcut cubic multiplication formulas</U>".