i need to expand (x+5)^6

iv got x^6+6(x)^5+15(x)^4+20(x)+15(x)+6(x)+5 Iv got that but i know iv missed out some powers as im not sure where there ment to go...Could someone help please?

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- Dec 17th 2007, 07:49 AM #1

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- Dec 17th 2007, 07:58 AM #2

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- Dec 17th 2007, 07:59 AM #3

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Hello, Chez_!

You didn't include the second term . . .

Expand: .$\displaystyle (x+{\color{red}5})^6 $

You should have: .$\displaystyle x^6 + 6(x^5)({\color{red}5^1}) + 15(x^4)({\color{red}5^2}) + 20(x^3)({\color{red}5^3}) + 15(x^2)({\color{red}5^4}) + 6(x)({\color{red}5^5}) + {\color{red}5^6} $

- Dec 17th 2007, 08:00 AM #4

- Dec 17th 2007, 08:04 AM #5

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- Dec 17th 2007, 08:07 AM #6

- Dec 17th 2007, 09:19 AM #7
It's long, but if you haven't been taught the fancier techniques there's nothing wrong with a little "elbow grease." Multiply it two terms at a time. Here's some markers for you so you can check your work:

$\displaystyle (x + 5)^6$

$\displaystyle = (x + 5)(x + 5)(x + 5)(x + 5)(x + 5)(x + 5)$

$\displaystyle = (x + 5)(x + 5)(x + 5)(x + 5)(x^2 + 10x + 5)$

$\displaystyle = (x + 5)(x + 5)(x + 5)(x^3 + 15x^2 + 75x + 125)$

$\displaystyle = (x + 5)(x + 5)(x^4 + 20x^3 + 150x^2 + 500x + 625)$

$\displaystyle = (x + 5)(x^5 + 25x^4 + 250x^3 + 1250x^2 + 3125x + 3125$

and finally:

$\displaystyle = x^6 + 30x^5 + 375x^4 + 2500x^3 + 9375x^2 +18750x + 15625$

-Dan