Square of 3 variables

Xcert SG

I forgot how to do this kind of expansion liao....anyone can help?

x,y,z are variables,raised to the power of 2.

(x+y+z)^2=?

eagle SG

Expand ((x+y) + z)²

(x+y)² + 2(x+y)(z) + z²

and then expand the first term again

skythewood SG

I forgot how to do this kind of expansion liao....anyone can help?

x,y,z are variables,raised to the power of 2.

(x+y+z)^2=?

(x+y+z)(x+y+z).

expand

Xcert SG

Thanks eagle and skyewood for ur help....I do vaguely remember there is some kind of formula to do this kind of expansion....especially if the power is very big...or did I remember wrongly?

skythewood SG

that's for big power, not for many variables.

(x +y)^n = (x^n) + nCr(x^(n-1))(y^1) +.......+ (y^n)

Xcert SG

that's for big power, not for many variables.

(x +y)^n = (x^n) + nCr(x^(n-1))(y^1) +.......+ (y^n)

Oh ya....anyway what's the name of this expansion formula?

purpledragon84 SG

binomial..? issit..? i duno.. lol..

eagle SG

ya binomial

O level A maths Binomial: Binomial Theorem
A level H2 Maths Binomial: Not yet

Xcert SG

ok....thanks to all for the help.

Ahm97sic SG

ya binomial

O level A maths Binomial: Binomial Theorem
A level H2 Maths Binomial: Not yet

Hi Eagle,

For your information, Binomial Expansion is in the new 2007 H2 Maths syllabus ie

Binomial expansion of n

(1+x)^n for any rational n

Condition for convergence of a binomial series

Proof by the method of mathematical induction

Regards,

ahm97sic

PS : Eagle, for your information, there is really a theorem that can be used to

expand XCert's question (x+y+z)^2. This theorem is known as the MULTINOMIAL

THEOREM.

(x+y+z)^2 = Summation [n!/(p!q!r!)] x^p y^q z^r

= x² + y² + z² + 2xy + 2xz + 2yz

(x+y+z)^3 = Summation [n!/(p!q!r!)] x^p y^q z^r

= x³ + y³ + z³ + 3x^2y + 3x²z + 3xy² + 3y²z + 3 xz² + 3 yz² + 6 xyz

Thank you for your kind attention.

Regards,

ahm97sic

Lee012lee SG

Xcert's Avatar

Mas Selamat, why learns maths huh ? you want to use maths to plan your escape from the detention camp, is it ?