Sentences with BINOMIAL-THEOREM
Check out our example sentences below to help you understand the context.Sentences
1
"The binomial theorem states that for any nonnegative integer n, the expansion of (a + b)^n can be given by the formula C(n, 0)a^n + C(n, 1)a^(n-1)b + C(n, 2)a^(n-2)b^2 + ... + C(n, n-1)ab^(n-1) + C(n, n)b^n."
2
"The binomial theorem is a fundamental concept in algebra and combinatorics."
3
"Using the binomial theorem, we can expand expressions such as (x + y)^3 or (2a - 3b)^4."
4
"The binomial theorem allows us to calculate the coefficients in the expansion of a binomial raised to a power."
5
"The binomial theorem is often used in probability theory to compute probabilities of events."
6
"The binomial theorem provides a way to simplify calculations involving binomial coefficients."
7
"The formula derived from the binomial theorem is also known as Pascal's triangle."
8
"The binomial theorem has applications in various fields including physics, engineering, and computer science."
9
"Understanding the binomial theorem is essential when studying calculus and series expansions."
10
"The binomial theorem was first discovered by the Chinese mathematician Zhu Shijie in the 13th century."
11
"The binomial theorem is closely related to the concept of combinatorial identities."
12
"Expanding (a - b)^n using the binomial theorem results in a similar expression with alternating signs."
13
"The proof of the binomial theorem can be established through mathematical induction."
14
"The binomial theorem provides a systematic way to expand binomial expressions for any given power."
15
"The binomial theorem is an extension of the concept of multiplying two binomials."
16
"The binomial theorem is an important tool in proving calculus formulas such as the power rule or the chain rule."
17
"The binomial theorem can be used to approximate values of large powers of binomials."
18
"The binomial theorem plays a crucial role in solving problems related to statistical distributions."
19
"The binomial theorem allows us to find specific terms in the expansion of a binomial expression."
20
"The proof of the binomial theorem involves using mathematical induction and the concept of combinatorics."
1
"The binomial theorem states that the coefficient of each term in the expansion of (a + b)^n can be found using the formula."
2
"According to the binomial theorem, the sum of the coefficients in the expansion of (a + b)^n is equal to 2^n."
3
"The binomial theorem is a fundamental concept in algebraic mathematics."
4
"Students often struggle with understanding the binomial theorem and its applications."
5
"The binomial theorem is used extensively in the field of probability and statistics."
6
"The binomial theorem allows us to expand expressions like (x + y)^n."
7
"The binomial theorem was first introduced by Isaac Newton."
8
"Applying the binomial theorem, we can easily expand expressions like (2a - 3b)^n."
9
"The binomial theorem provides a systematic way of expanding binomial expressions."
10
"Understanding the binomial theorem is crucial for solving complex mathematical problems."
