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The binomial expansion of ((x^2 + y)^4) can be expressed using the Binomial Theorem, which states that ((a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k). For ((x^2 + 0)^4), the expansion simplifies to just one term: ((x^2)^4 = x^8). Thus, the complete expansion for ((x^2)^4) is simply (x^8).
If the expression were ((x^2 + y)^4), the expansion would yield: (x^8 + 4x^6y + 6x^4y^2 + 4x^2y^3 + y^4).
What else can I help you with?
What is a binomial coefficient?
A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.
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 a binominal theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
What is the correct expansion of the binomial x plus y to the 6th power?
X + Y⁶X + Y * Y * Y * Y * Y * Y
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 a binomial coefficient?
A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.
What is the relationship between the binomial expansion and binomial distribution?
First i will explain the binomial expansion
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).
When is the 24 x 24 expansion farm available?
Farmville's 24 x 24 expansion will be available March of 2010
What is a binominal theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
How do you find the coefficients of the terms in the binomial expansion?
The coefficient of x^r in the binomial expansion of (ax + b)^n isnCr * a^r * b^(n-r)where nCr = n!/[r!*(n-r)!]
What is the correct expansion of the binomial x plus y to the 6th power?
X + Y⁶X + Y * Y * Y * Y * Y * Y
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 The expansion of a binomial that involves a coefficient found by combinations?
Binomial Theorum
What is binomial expansion?
Sounds pretty sexy, eh? See link. http://en.wikipedia.org/wiki/Binomial_expansion
Validity of binomial expansion for n less than 0?
The binomial expansion is valid for n less than 1.
How is the pascal triangle and the binomial expansion related?
If the top row of Pascal's triangle is "1 1", then the nth row of Pascals triangle consists of the coefficients of x in the expansion of (1 + x)n.
