perplexus.info :: Just Math : Septic Factorization

Septic Factorization (Posted on 2015-06-07)

Factorize: (a+b)⁷ - a⁷ - b⁷

Note: For an extra challenge, solve this puzzle without the aid of a computer program or an online calculator.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Correction, presumably not fully factored

| Comment 2 of 5 |

Well, that last answer is not correct. I hope no children read it. In a binomial expansion, the coefficients are given by pascal's triangle.

So (a+b)^7 = a^7 + 7a^6b+ 21a^5b^2 + 35a^4b^3 + 35a^3b^4 + 21a^2b^5 + 7ab^6 +b^7

So (a+b)^7 -a^7 - b^7 = 7ab(a^5+ 3a^4b + 5a^3b^2 + 5a^2b^3 + 3ab^4 + b^5)

I leave it to others to take it from here

Edited on June 7, 2015, 7:39 pm

Posted by Steve Herman on 2015-06-07 19:38:08

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