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What is the expansion of the binomial?

What is the expansion of the binomial?

A binomial is an algebraic expression with two terms. For example, a + b, x – y, etc are binomials. We have a set of algebraic identities to find the expansion when a binomial is raised to exponents 2 and 3. For example, (a + b)2 = a2 + 2ab + b2.

What is binomial theorem in physics?

binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form.

What does the binomial theorem state?

The Binomial Theorem states the algebraic expansion of exponents of a binomial, which means it is possible to expand a polynomial (a + b) n into the multiple terms.

Who invented binomial expansion?

Isaac Newton
Isaac Newton is generally credited with the generalized binomial theorem, valid for any rational exponent.

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Why was binomial theorem created?

The binomial theorem provides a simple method for determining the coefficients of each term in the expansion of a binomial with the general equation (A + B)n. Developed by Isaac Newton, this theorem has been used extensively in the areas of probability and statistics .

What is binomial induction?

It is a method used to prove simple or complicated statements in Mathematics. Binomial theorem helps in expanding the expression [x + y] n. For proving the statement of the binomial, we make use of this mathematical induction.

How do you prove induction?

The inductive step in a proof by induction is to show that for any choice of k, if P(k) is true, then P(k+1) is true. Typically, you’d prove this by assum- ing P(k) and then proving P(k+1). We recommend specifically writing out both what the as- sumption P(k) means and what you’re going to prove when you show P(k+1).

How does binomial theorem work?

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The binomial theorem is an algebraic method of expanding a binomial expression. Essentially, it demonstrates what happens when you multiply a binomial by itself (as many times as you want). It would take quite a long time to multiply the binomial (4x+y) ( 4 x + y ) out seven times.