SOLUTION: How to factorise: a^3+b^3+3a^2b+3ab^2 Any help is appreciated!

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Question 1067827: How to factorise: a^3+b^3+3a^2b+3ab^2
Any help is appreciated!
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Binomial Theorem? Pascal's Triangle? If you are not sure how to use them for help, try polynomial Division. Divide your cubic expression by a%2Bb and you should be able to find a quotient which is a more easily factorable quadratic expression. 


          a^2     2ab       b^2
     _______________________________________
a+b  |    a^3  +  3a^2*b  +3b^2a  +  b^3
     |
     |    a^3     a^2*b
      ------------------
           0      2a^2*b   3b^2*a 
                  2a^2*b   2a*b^2
                 ----------------
                    0       ab^2     b^3
                            ab^2     b^3
                           ---------------
                             0        0

That quotient is a%5E2%2B2ab%2Bb%5E2.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
a%5E3+%2B+b%5E3+%2B+3a%5E2b+%2B+3ab%5E2 = %28a+%2B+b%29%5E3.


It is  ONE OF THE BASIC  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 cube of the sum formula is                 %28a+%2B+b%29%5E3+=+a%5E3+%2B+3a%5E2%2Ab+%2B+3a%2Ab%5E2+%2B+b%5E3.
      For details and examples of applications of this formula see the lesson The cube of the sum formula


2. The cube of the difference formula is     %28a+-+b%29%5E3+=+a%5E3+-+3a%5E2%2Ab+%2B+3a%2Ab%5E2+-+b%5E3.
      For details and examples of applications of this formula see the lesson The cube of the difference formula


3. The sum of cubes formula is                       a%5E3+%2B+b%5E3+=+%28a+%2B+b%29%2A%28a%5E2+-+ab+%2B+b%5E2%29.
      For details and examples of applications of this formula see the lesson The sum of cubes formula

4. The difference of cubes formula is           a%5E3+-+b%5E3+=+%28a+-+b%29%2A%28a%5E2+%2B+ab+%2B+b%5E2%29.
      For details and examples of applications of this formula see the lesson The difference of cubes formula



Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

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