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In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by The expansion is given by ( a + b + c ) n = ∑ i , j , k i + j + k = n ( n i , j , k ) a i b j c k , {\displaystyle (a+b+c)^{n}=\sum _{{i,j,k} \atop {i+j+k=n}}{n \choose i,j,k}\,a^{i}\,b^{\;\!j}\;\!c^{k},}
For instance, the polynomial x 2 + 3x + 2 is an example of this type of trinomial with n = 1. The solution a 1 = −2 and a 2 = −1 of the above system gives the trinomial factorization: x 2 + 3x + 2 = (x + a 1)(x + a 2) = (x + 2)(x + 1). The same result can be provided by Ruffini's rule, but with a more complex and time-consuming process.
Trinomial coefficient may refer to: coefficients in the trinomial expansion of (a + b + c) n. coefficients in the trinomial triangle and expansion of (x 2 + x + 1) n
Vieta's formulas are frequently used with polynomials with coefficients in any integral domain R.Then, the quotients / belong to the field of fractions of R (and possibly are in R itself if happens to be invertible in R) and the roots are taken in an algebraically closed extension.
The middle entries of the trinomial triangle 1, 1, 3, 7, 19, 51, 141, 393, 1107, 3139, … (sequence A002426 in the OEIS) were studied by Euler and are known as central trinomial coefficients. The only known prime central trinomial coefficients are 3, 7 and 19 at n = 2, 3 and 4. The -th central trinomial coefficient is given by
Kyuranger is considered the fifth space-themed series [a] whose primary motifs are constellations and Greco-Roman mythology, and it is also the first Super Sentai series to introduce nine regular members in the beginning instead of five or fewer like previous installments. The team later gains three additional members, increasing the number to ...
Originally, many thước of varying lengths were in use in Vietnam, each used for different purposes. According to Hoàng Phê (1988), [1] the traditional system of units had at least two thước of different lengths before 1890, [2] the thước ta (lit. "our ruler") or thước mộc ("wooden ruler"), equal to 0.425 metres (1 ft 4.7 in), and the thước đo vải ("ruler for measuring ...
The Vietnamese Wikipedia initially went online in November 2002, with a front page and an article about the Internet Society.The project received little attention and did not begin to receive significant contributions until it was "restarted" in October 2003 [3] and the newer, Unicode-capable MediaWiki software was installed soon after.