- #1

- 202

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Show that (x + a + b)^7 - x^7 - a^7 - b^7 is divisble by

x^2 + (a + b)x +ab.

- Thread starter Hyperreality
- Start date

- #1

- 202

- 0

Show that (x + a + b)^7 - x^7 - a^7 - b^7 is divisble by

x^2 + (a + b)x +ab.

- #2

drag

Science Advisor

- 1,062

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You can always solve the entire excercise...

Live long and prosper.

- #3

- 313

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Hint:Show that (x + a + b)^7 - x^7 - a^7 - b^7 is divisble by x^2 + (a + b)x +ab.

Notice that (x+a) and (x+b) are the 2 factors of x^2 + (a + b)x +ab.

So it is equivalent to show that (x + a + b)^7 - x^7 - a^7 - b^7 is divisible by both (x+a) and (x+b).

Let f(x) = (x + a + b)^7 - x^7 - a^7 - b^7

.....

.....

.....

.....

Can you continue from here?

Hope this help.

- #4

- 24

- 0

eg. (x+a)^2=x^2+2xa+a^2

maybe rewrite some terms then and you will see that it is divisible by x^2 + (a + b)x +ab

- #5

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

Writing it out however... *shudder* I wouldn't wish writing out a trinomial to the 7th power to anyone!

Hurkyl

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