What is the expansion of the binomial?
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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.
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?
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.