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Which statement about the simplified binomial expansion of (a plus b)n where n is a positive integer is true?
Wiki User
∙ 9y ago
The question implies that there is a list of statements of which one or more are true. In such circumstances would it be too much to expect that you make sure that there is something that is following?
Wiki User
∙ 9y ago
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Define binomial theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).
What is the relationship between Pascal triangle and binomial theorem?
The coefficients of the binomial expansion of (1 + x)n for a positive integer n is the nth row of Pascal's triangle.
What is binomial expansion theorem?
We often come across the algebraic identity (a + b)2 = a2 + 2ab + b2. In expansions of smaller powers of a binomial expressions, it may be easy to actually calculate by working out the actual product. But with higher powers the work becomes very cumbersome.The binomial expansion theorem is a ready made formula to find the expansion of higher powers of a binomial expression.Let ( a + b) be a general binomial expression. The binomial expansion theorem states that if the expression is raised to the power of a positive integer n, then,(a + b)n = nC0an + nC1an-1 b+ nC2an-2 b2+ + nC3an-3 b3+ ………+ nCn-1abn-1+ + nCnbnThe coefficients in each term are called as binomial coefficients and are represented in combination formula. In general the value of the coefficientnCr = n!r!(n-r)!It may be interesting to note that there is a pattern in the binomial expansion, related to the binomial coefficients. The binomial coefficients at the same position from either end are equal. That is,nC0 = nCn nC1 = nCn-1 nC2 = nCn-2 and so on.The advantage of the binomial expansion theorem is any term in between can be figured out without even actually expanding.Since in the binomial expansion the exponent of b is 0 in the first term, the general term, term is defined as the (r+1)th b term and is given by Tr+1 = nCran-rbrThe middle term of a binomial expansion is [(n/2) + 1]th term if n is even. If n is odd, then terewill be two middle terms which are [(n+1)/2]th and [(n+3)/2]th terms.
If the constant term of (x3 plus ax2)5 is equal to -270 then what is a?
Both terms in the binomial have positive exponents of x and so it is not possible for there to be a constant term in its expansion. If the second term is a negative power then it is not possible to tell whether it should be (a/x^2) or 1/(ax^2) which will yield different answers.
How can you turn the difference of two positive numbers is always positive into a false statement?
By subtracting a positive number from itself. 3 - 3 = 0
Define binomial theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).
What is the relationship between Pascal triangle and binomial theorem?
The coefficients of the binomial expansion of (1 + x)n for a positive integer n is the nth row of Pascal's triangle.
What is binomial expansion theorem?
We often come across the algebraic identity (a + b)2 = a2 + 2ab + b2. In expansions of smaller powers of a binomial expressions, it may be easy to actually calculate by working out the actual product. But with higher powers the work becomes very cumbersome.The binomial expansion theorem is a ready made formula to find the expansion of higher powers of a binomial expression.Let ( a + b) be a general binomial expression. The binomial expansion theorem states that if the expression is raised to the power of a positive integer n, then,(a + b)n = nC0an + nC1an-1 b+ nC2an-2 b2+ + nC3an-3 b3+ ………+ nCn-1abn-1+ + nCnbnThe coefficients in each term are called as binomial coefficients and are represented in combination formula. In general the value of the coefficientnCr = n!r!(n-r)!It may be interesting to note that there is a pattern in the binomial expansion, related to the binomial coefficients. The binomial coefficients at the same position from either end are equal. That is,nC0 = nCn nC1 = nCn-1 nC2 = nCn-2 and so on.The advantage of the binomial expansion theorem is any term in between can be figured out without even actually expanding.Since in the binomial expansion the exponent of b is 0 in the first term, the general term, term is defined as the (r+1)th b term and is given by Tr+1 = nCran-rbrThe middle term of a binomial expansion is [(n/2) + 1]th term if n is even. If n is odd, then terewill be two middle terms which are [(n+1)/2]th and [(n+3)/2]th terms.
Which statement BEST identifies a positive effect of westward expansion in the years before the Civil War?
Westward expansion led to an economic "boom" in the Midwest, as new cities and markets were connected by rail and canals.
What is Binomial Expansion and how does it relate to Pascal's Triangle?
The binomial expansion is the expanded form of the algebraic expression of the form (a + b)^n.There are slightly different versions of Pascal's triangle, but assuming the first row is "1 1", then for positive integer values of n, the expansion of (a+b)^n uses the nth row of Pascals triangle. If the terms in the nth row are p1, p2, p3, ... p(n+1) then the binomial expansion isp1*a^n + p2*a^(n-1)*b + p3*a^(n-2)*b^2 + ... + pr*a^(n+1-r)*b^(r-1) + ... + pn*a*b^(n-1) + p(n+1)*b^n
If the constant term in the factoring of a trinomial is positive then the signs in both binomial factors will be negative?
Not necessarily. They could both be positive.
Is this a positive statement or normative statement The minimum wage creates unemployment among young and unskilled workers?
It is a positive statement.
What is an example of a positive prejudicial statement?
A positive prejudicial statement is a statement that relies on stereotypes, but does not say anything negative about the group. For example, saying Asians are good at math would be a positive prejudicial statement.
What is an example of a positive statement?
A positive statement is a philosophical term for statements that simply state how things are without moral implications. An example of a positive statement would be "the grass is green".
Turbine differential expansion should be positive or negative?
Turbine diff expansion can be positive or negative and depends on the convention used. The usual convention is that positive expansion is rotor expanding faster (hotter) than fixed components. Expansion is dictated by steam flow, gland steam temperatures etc
Is this statement Inflation is more harmful to the economy than unemployment a positive statement?
equality is more important than efficiency. Is that a positive or normative statement?
What is an example of a prejudicial statement?
A positive prejudicial statement is a statement that relies on stereotypes, but does not say anything negative about the group. For example, saying Asians are good at math would be a positive prejudicial statement.
