# Math Help - finind coeffitient

1. ## finind coeffitient

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?

2. Code:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
That mean anything to you ?

3. Hello, Chez_!

You didn't include the second term . . .

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

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

4. not really lol

5. do you know anything about the binomial expansion?

6. Originally Posted by bobak
do you know anything about the binomial expansion?
Or Pascal's triangle (which is what bobak first showed you)?

7. Originally Posted by Chez_
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?
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:
$(x + 5)^6$

$= (x + 5)(x + 5)(x + 5)(x + 5)(x + 5)(x + 5)$

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

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

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

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

and finally:
$= x^6 + 30x^5 + 375x^4 + 2500x^3 + 9375x^2 +18750x + 15625$

-Dan