-
Finished your HSC? Check out our University Discussion, Non-School forums or help out next year's HSC students! -
YOU can help the next generation of students in the community! Share your trial papers and notes on our Notes & Resources page
Binomial Theorem help (1 Viewer)
- Thread starter fullonoob
- Start date
- Joined
- Feb 16, 2005
- Messages
- 8,393
- Gender
- Male
- HSC
- 2006
(3 - x)(4 + x)5 = 3(4 + x)5 - x(4 + x)5
For the (4 + x)5, we want the
- x² term because when we multiply it by x from (3 - x), we end up with an x³
- x³ term because when we multiply it by 3 from (3 - x), we end up with an x³
The x² term in (4 + x)5 is 5C24³x² = 640x²
The x³ term in (4 + x)5 is 5C34²x³ = 160x³
When we multiply these individual terms by (3 - x), we are only interested in the x³ terms only (ignore the rest), so we only want: 640x²(-x) and 160x³(3)
Hence the co-efficient of x³ is: - 640 + 480 = -160
For the (4 + x)5, we want the
- x² term because when we multiply it by x from (3 - x), we end up with an x³
- x³ term because when we multiply it by 3 from (3 - x), we end up with an x³
The x² term in (4 + x)5 is 5C24³x² = 640x²
The x³ term in (4 + x)5 is 5C34²x³ = 160x³
When we multiply these individual terms by (3 - x), we are only interested in the x³ terms only (ignore the rest), so we only want: 640x²(-x) and 160x³(3)
Hence the co-efficient of x³ is: - 640 + 480 = -160
(3-x)(4+x)^5
In the same manner as the previous answer. Expand out the question.
3(4+x)5 - x(4+x)5
To get the term with x4 for the first half of the expression use the binomial theorem:
3.5C1.41. x4
and the second half is the binomial theorem x3 term because it is multiplied by x.
-x.5C2.42.x3
Thus coeff = 3.5.4 - 100.16 = -100 (if I did the maths right - It's late)
(1-y)^2(3-y)^7
In this one you need to look at the combinations of coefficients that make 4.
coeff( y0 x y4) + coeff(y1 x y3) + coeff(y2 x y2)
AND that's it because the first expression is power 2.
But since it's nearly midnight, my brain isn't working so well, so maybe you can figure that one out for yourself
In the same manner as the previous answer. Expand out the question.
3(4+x)5 - x(4+x)5
To get the term with x4 for the first half of the expression use the binomial theorem:
3.5C1.41. x4
and the second half is the binomial theorem x3 term because it is multiplied by x.
-x.5C2.42.x3
Thus coeff = 3.5.4 - 100.16 = -100 (if I did the maths right - It's late)
(1-y)^2(3-y)^7
In this one you need to look at the combinations of coefficients that make 4.
coeff( y0 x y4) + coeff(y1 x y3) + coeff(y2 x y2)
AND that's it because the first expression is power 2.
But since it's nearly midnight, my brain isn't working so well, so maybe you can figure that one out for yourself
bored of sc
Active Member
- Joined
- Nov 10, 2007
- Messages
- 2,314
- Gender
- Male
- HSC
- 2009
56+55.33+53.35+36 = 25(212+1)fullonoob said:
5-3 = 2 that's the relationship we could be trying to establish
I'll come back later.