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What is the second term in the binomial expansion of (2x−3y)12 ?

Recall the binomial theorem:

Group of answer choices

73728x11y1


−73728x11y


−608256x10y2


608256x10y2

Respuesta :

The option that gives the correct value of the second term is;

Option B; -73728x¹¹y

We are given the expression;

(2x - 3y)¹²

Now we want to find the second term using binomial expansion.

  • In binomial theorem, we have the following expressions;

(x + y)² = x² + 2xy + y²

(x - y)³ = x³ - 3x²y + 3xy² + y³

(x - y)⁴ = x⁴ - 4x³y + 6x²y² - 4xy³ + y⁴

(x - y)¹² = x¹² - x¹¹y + x¹⁰y² - x⁹y³ + ....

Now applying this same system above to our question gives us;

(2x - 3y)¹² = 4096x¹² - 73728x¹¹y + 608256x¹⁰y² - 3041280x⁹y³ + ........

Thus, our second term here is; -73728x¹¹y

In conclusion, the correct option that gives the second term is Option B.

Read more at; https://brainly.com/question/24102756

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