10. Combinatorics & Probability

Find the term indicated in each expansion. (x − 1)⁹; fifth term

Find the term indicated in each expansion. (2x + y)⁶; third term

Write the first three terms in each binomial expansion, expressing the result in simplified form. (y³ − 1)²⁰

Write the first three terms in each binomial expansion, expressing the result in simplified form. (x² + 1)¹⁶

Write the first three terms in each binomial expansion, expressing the result in simplified form. (x - 2y)¹⁰

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

Find f(x + h) − f(x)/h and simplify. f(x) = x⁴+7

Use the Binomial Theorem to expand each expression and write the result in simplified form. (x^1/3 +x^-1/3)³

Use the Binomial Theorem to expand each expression and write the result in simplified form. (x³ +x^-2)⁴

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (2a + b)⁶

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (3x − y)⁵

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (c+2)⁵

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (2x³ − 1)⁴