(1-x)9
= 1+9x - 36x2 + 84x3 - 126x4
not sure if the answer should begin with a plus or a minus..
please clarify
thanks
Assuming you mean $\displaystyle (1-x)^9$ the first term is positive as you put.
For every even power of x you will have a + sign and for every odd power of x will have a - sign (hence your signs are wrong from the second term onwards)
From the binomial expansion on the first term $\displaystyle {9 \choose 0}1^9(-x)^0 = 1$
yep i mean but dont know how to do the signs on my keyboard)
thanks for that so is this correct now??:
= 1+9x + 36x2 + 84x3 + 126x4
despite having the result, what method would you use to get to the result as the method I used was the same as method I would use if calculating (1+x)7 any ideas?
thanks for your guidance
What you did was wrong because $\displaystyle (1-x)^9$ must contain 9th power.
You might use this to learn about yourself
Binomial theorem
Therefore, the answer should be:
$\displaystyle 1-9x+36x^2-84x^3+126x^4-126x^5+84x^6-36x^7+9x^8-x^9$
See the red parts. The simplest method is to use the binomial theorem
$\displaystyle (a+b)^n = \sum^n_{i=0} {n \choose i}a^{n-i}b^i$
To find and given term sub in the appropriate value of i. To find the 7th term of this sequence would use $\displaystyle n=9$ and $\displaystyle i=7$
No, you need to pay more attention to your signs (also 1 is a term so you have 5 terms there )
The first three terms are given by $\displaystyle (1-x)^9 = {9 \choose 0}1^9(-x)^0 + {9 \choose 1}1^8(-x)^1 + {9 \choose 2}1^7(-x)^2$
Which simplifies to $\displaystyle 1 - 9x + 36x^2$