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Use the Binomial Theorem to write the expansion of (2a-4b)^(5)

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Final answer:

To expand (2a-4b)^(5) using the Binomial Theorem, substitute n = 5 into the formula (a + b)^(n). This will give you a sum of terms, each multiplied by the corresponding binomial coefficient. Simplify the expression to obtain the expanded form of (2a-4b)^(5).

Step-by-step explanation:

To expand the expression (2a-4b)5 using the Binomial Theorem, we use the formula:
(a + b)n = C(n,0)anb0 + C(n,1)an-1b1 + C(n,2)an-2b2 + ... + C(n,n)a0bn

Where C(n,r) is the binomial coefficient, which represents the number of ways to choose r items from a set of n items. In this case, n = 5. The expansion of (2a-4b)5 is:

C(5,0)(2a)5(-4b)0 + C(5,1)(2a)4(-4b)1 + C(5,2)(2a)3(-4b)2 + C(5,3)(2a)2(-4b)3 + C(5,4)(2a)1(-4b)4 + C(5,5)(2a)0(-4b)5

Simplifying the equation, we get:

1(2a)5(-4b)0 + 5(2a)4(-4b)1 + 10(2a)3(-4b)2 + 10(2a)2(-4b)3 + 5(2a)1(-4b)4 + 1(2a)0(-4b)5

This can be simplified further:

-32a5 + 160a4b - 320a3b2 + 320a2b3 - 160ab4 + 32b5

User DGuntoju
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