Square of 3 variables
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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=?
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Expand ((x+y) + z)²
to
(x+y)² + 2(x+y)(z) + z²
and then expand the first term again
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Originally posted by Xcert:
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
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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?
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that's for big power, not for many variables.
(x +y)^n = (x^n) + nCr(x^(n-1))(y^1) +.......+ (y^n)
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Originally posted by skythewood:
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? -
binomial..? issit..? i duno.. lol..
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ya binomial
O level A maths Binomial: Binomial Theorem
A level H2 Maths Binomial: Not yet -
ok....thanks to all for the help.
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Originally posted by eagle:
ya binomial
O level A maths Binomial: Binomial Theorem
A level H2 Maths Binomial: Not yetHi 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 + 3x2y + 3x2z + 3xy2 + 3y2z + 3 xz2 + 3 yz2 + 6 xyz
Thank you for your kind attention.
Regards,
ahm97sic
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Mas Selamat, why learns maths huh ? you want to use maths to plan your escape from the detention camp, is it ?
