• Best of luck to the class of 2024 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • YOU can help the next generation of students in the community!
    Share your trial papers and notes on our Notes & Resources page
MedVision ad

Expanding with power 4 (how)? (1 Viewer)

Lurch

New Member
Joined
Feb 16, 2004
Messages
13
Location
Sydney (Hobbit land)
is there an easy way of expanding (x+y)^4 without going through the process of tediously doing (x+y)(x+y)(x+y)(x+y) OR Without going (x+y)^2 multiplied by (x+y)^2 ?
 

Lurch

New Member
Joined
Feb 16, 2004
Messages
13
Location
Sydney (Hobbit land)
I suppose pascals triangle but I was wondering if there is any easy method (even though pascals triangle is easy) :)
Just curious..
 

:: ck ::

Actuarial Boy
Joined
Jan 1, 2003
Messages
2,414
Gender
Male
HSC
2004
ok for 2u... mayb u can think of

just expanding it as (x+y)^2
then square it again?

or u can use binomial theorem/pascals triangle...
 

kpq_sniper017

Member
Joined
Dec 18, 2003
Messages
672
if you're a 3U student, then binomial theorem is the best.

(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

if you really need to remember it, then remember:
1. the powers always add up to 4 (for ^4)
2. as powers of x increase, powers of y decrease and vice versa
3. and for ^4, the coefficients are: 1, 4, 6, 4 and 1
 

Affinity

Active Member
Joined
Jun 9, 2003
Messages
2,062
Location
Oslo
Gender
Undisclosed
HSC
2003
By inspection... in other words.. do it a few(~100) times then you should remember it
 

~*HSC 4 life*~

Active Member
Joined
Aug 15, 2003
Messages
2,411
Gender
Undisclosed
HSC
N/A
Originally posted by pcx_demolition017
i don't think there is anything easier than binomial theorem.
:)
to my knowledge.

Yeah, binomial theorem is "easy" hahaha
 

Calculon

Mohammed was a paedophile
Joined
Feb 15, 2004
Messages
1,743
Gender
Undisclosed
HSC
N/A
Originally posted by ~*HSC 4 life*~
Yeah, binomial theorem is "easy" hahaha
Those inverted commas are unnecessary
 

Collin

Active Member
Joined
Jun 17, 2003
Messages
5,084
Gender
Undisclosed
HSC
N/A
Is pascal's triangle 2 unit? I thought it was 3 unit.

Anyway, assuming pascals' is not 2 unit, you really have no alternative but to manually expand.

Another method, if you're quick at picking up mathematical concepts, is to simply memorise the binomial expansion rules from a 3 unit textbook. But expanding to the power of 4 doesn't take too long, even by slow manual expansion. If they ask you for (p - q)^32 or something, then I'd be slightly worried.
 

Calculon

Mohammed was a paedophile
Joined
Feb 15, 2004
Messages
1,743
Gender
Undisclosed
HSC
N/A
Originally posted by ~*HSC 4 life*~
pppft just because you're a maths genius :p
I don't claim to be a maths genius. If you knew some of the people at my school you would see why.
 

kpq_sniper017

Member
Joined
Dec 18, 2003
Messages
672
just for interest....
are you allowed to use 3U methods in 2U?
e.g. if a question said:

hence or <u>otherwise</u> expand (x+y)^4 - note the "otherwise" in a 2U test

does that mean you could use binomial theorem??
 

CM_Tutor

Moderator
Moderator
Joined
Mar 11, 2004
Messages
2,642
Gender
Male
HSC
N/A
In this paricular case, how would they know? Suppose a question was:

1 (a). Expand (x + y)<sup>2</sup>

(b). Hence, or otherwise, expand (x + y)<sup>4</sup>

and you wrote

1(a) (x + y)<sup>2</sup> = x<sup>2</sup> + 2xy + y<sup>2</sup>

1(b) (x + y)<sup>4</sup> = x<sup>4</sup> + 4x<sup>3</sup>y + 6x<sup>2</sup>y<sup>2</sup> + 4xy<sup>3</sup> + y<sup>4</sup>

how would they know? - even if the question only said 'hence', could they really penalise this answer?

Obviously, they'd know you did 'hence' if you wrote:

(x + y)<sup>4</sup> = [(x + y)<sup>2</sup>]<sup>2</sup> = (x<sup>2</sup> + 2xy + y<sup>2</sup>)<sup>2</sup> = (x<sup>2</sup> + 2xy)<sup>2</sup> + 2(x<sup>2</sup> + 2xy) * y<sup>2</sup> + (y<sup>2</sup>)<sup>2</sup> = ...

Similarly, they'd know you used the binomial theorem if <sup>4</sup>C<sub>k</sub>'s started to appear. In practice, 'hence or otherwise' only starts to appear once you must be showing enough working for them to be able to tell.

As for your more general question, it's better to stick to 2u methods if you can, but if you can't, a 3u answer beats no answer any day.
 

Ragerunner

Your friendly HSC guide
Joined
Apr 12, 2003
Messages
5,472
Location
UNSW
Gender
Male
HSC
2003
Ok.....Is it me or is the binomial theorm freaky? Or am I looking at the wrong one?

 

CM_Tutor

Moderator
Moderator
Joined
Mar 11, 2004
Messages
2,642
Gender
Male
HSC
N/A
Actually, that's an application of the binomial theorem - the theorem itself is just <sup>n</sup>C<sub>r</sub> = n! / r!(n - r)!
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top