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)

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Solution

| Comment 1 of 5

By the binomial expansion:

(a+b)^7 -a^7 -b^7 = a^6b + a^5b^2 + . . . + ab^6

= ab(a^5 + a^4b + . . . +b^5)

= ab(a + b)^5

Not a computer in sight!

Posted by JayDeeKay on 2015-06-07 15:52:11

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