Introduction
Binomial Theorem is the method of expanding an expression that has been raised to a finite power. In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
Consider the expansion of (x + y)5
(x + y)5 = (x + y)(x + y)(x + y)(x + y)(x + y)
The first term is obtained by multiplying the xs in the five brackets, there is only one way to doing this.
(x + y)n = xn + nxn-1y + n(n-1)/2! xn-2y2 + n(n-1)(n-2)/3! xn-3y3 + ...n(n-1)(n-2)...(n-r+1)/r! xn-ryr + ...yn
It can be shown that the binomial formula holds for positive, negative, integral or any rational value of n, provided there is a restriction on the values of x and y in the expansion of (x + y)n. We shall however consider only the binomial expansion formula for a positive integral n.
Binomial Theorem is the method of expanding an expression that has been raised to a finite power. In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
Consider the expansion of (x + y)5
(x + y)5 = (x + y)(x + y)(x + y)(x + y)(x + y)
The first term is obtained by multiplying the xs in the five brackets, there is only one way to doing this.
(x + y)n = xn + nxn-1y + n(n-1)/2! xn-2y2 + n(n-1)(n-2)/3! xn-3y3 + ...n(n-1)(n-2)...(n-r+1)/r! xn-ryr + ...yn
It can be shown that the binomial formula holds for positive, negative, integral or any rational value of n, provided there is a restriction on the values of x and y in the expansion of (x + y)n. We shall however consider only the binomial expansion formula for a positive integral n.
Introduction
Binomial Theorem is the method of expanding an expression that has been raised to a finite power. In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
Consider the expansion of (x + y)5
(x + y)5 = (x + y)(x + y)(x + y)(x + y)(x + y)
The first term is obtained by multiplying the xs in the five brackets, there is only one way to doing this.
(x + y)n = xn + nxn-1y + n(n-1)/2! xn-2y2 + n(n-1)(n-2)/3! xn-3y3 + ...n(n-1)(n-2)...(n-r+1)/r! xn-ryr + ...yn
It can be shown that the binomial formula holds for positive, negative, integral or any rational value of n, provided there is a restriction on the values of x and y in the expansion of (x + y)n. We shall however consider only the binomial expansion formula for a positive integral n.
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