Question

Use the Binomial Theorem to expand the power of a binomial.

A. 4x5+3x4
B. 4x5+12x4+12x3+4x2
C.1024x5+3840x4+5760x3+4320x2+1620x+243
D.1024x5+3072x4+4608x3+3456x2+1296x+1944

Answer 1

To expand the power of a binomial using the Binomial Theorem, find each term of the expansion by applying the theorem formula. For the binomial 4x^5 + 3x^4, the expansion is 4x^5 + 20x^4.

Step-by-step explanation:

To expand the power of a binomial using the Binomial Theorem, we need to find each term of the expansion. The Binomial theorem states that (a + b)^(n) = C(n, 0)a^(n)b^(0) + C(n, 1)a^(n-1)b^(1) + C(n, 2)a^(n-2)b^(2) + ... + C(n, n)a^(0)b^(n), where C(n, k) is the binomial coefficient, given by C(n, k) = n!/(k!(n-k)!). Let's apply this theorem to the binomial 4x^5 + 3x^4:

1. First, let's find the coefficient of the first term. Using C(5, 0) = 1, the first term is 1 * (4x^5) * (3)^0 = 4x^5.
2. Next, let's find the coefficient of the second term. Using C(5, 1) = 5, the second term is 5 * (4x^4) * (3)^1 = 20x^4.
3. Since there are no more terms, the expansion of the binomial 4x^5 + 3x^4 using the Binomial Theorem is 4x^5 + 20x^4.