Final answer:
The expansion of (2a-4b)^5 using the Binomial Theorem results in 32a^5 - 320a^4b + 1280a^3b^2 - 2560a^2b^3 + 2560ab^4 - 1024b^5.
Step-by-step explanation:
The process of expanding (2a-4b)^5 using the Binomial Theorem involves summing up the series expansion terms where each term is a product of a binomial coefficient and the corresponding powers of 2a and -4b.
The Binomial Theorem states in general that:
(a + b)^n = a^n + n(a^(n-1))b + n(n-1)/2! (a^(n-2))b^2 + n(n-1)(n-2)/3! (a^(n-3))b^3 + ...
Applying this to (2a-4b)^5 gives:
(2a)^5 + 5((2a)^4)(-4b) + 10((2a)^3)(-4b)^2 + 10((2a)^2)(-4b)^3 + 5(2a)(-4b)^4 + (-4b)^5
Which simplifies to:
- 32a^5
- -320a^4b
- +1280a^3b^2
- -2560a^2b^3
- +2560ab^4
- -1024b^5