10. Combinatorics & Probability

In Exercises 39–48, find the term indicated in each expansion. (x − 1)^9; fifth term

In Exercises 39–48, find the term indicated in each expansion. (2x + y)^6; third term

In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form. (y³ − 1)^20

In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form. (x² + 1)^16

In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form. (x - 2y)^10

In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form. (x+2)^8

Use the Binomial Theorem to expand and then simplify the result: (x² +x+ 1)³.

Find the middle term in the expansion of (3/x + x/3)^10

n Exercises 53–54, find f(x + h) − f(x)/h and simplify. f(x) = x^4+7

In Exercises 49–52, use the Binomial Theorem to expand each expression and write the result in simplified form. (x^1/3 +x^-1/3)^3

In Exercises 49–52, use the Binomial Theorem to expand each expression and write the result in simplified form. (x^3 +x^-2)^4

In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form. (2a + b)^6

In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form. (3x − y)^5

In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form. (c+2)^5

In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form. (2x³ − 1)^4