9. Sequences, Induction, and Probability

Evaluate a Binomial Coefficient

The Binomial Theorem

Pascal's Triangle and the Binomial Coefficients

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

Use the Binomial Theorem to expand the binomial and express the result in simplified form. ((x^2)-1)^4

Binomial Expansion Finding Coefficient

The Binomial Theorem - Example 2

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

The Binomial Theorem and Pascal's Triangle

In Exercises 1–8, evaluate the given binomial coefficient. <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/2642c7e7a56ffb0a-1678244022654.jpg" style="width: 141px;">

Use the Binomial Theorem to expand the binomial and express the result in simplified form. (2x+1)^3

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

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

In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form. (x+2)³

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 39–48, find the term indicated in each expansion. (x²+y³)^8; sixth term

Write the first three terms in the binomial expansion, expressing the result in simplified form. (x-3)^9

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. (c+2)^5

In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form. (x − 1)^5

Evaluating Binomial Coefficients

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

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

Thinkwell's College Algebra: Binomial Coefficients

Evaluate the given binomial coefficient
11
8

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

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

In Exercises 1–8, evaluate the given binomial coefficient. <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/b9dc7498d45da53b-1678243988451.jpg" style="width: 153px;">

Find the term indicated in the expansion. (2x-3)^6; fifth term

In Exercises 1–8, evaluate the given binomial coefficient. <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/7e558ca4bc980c04-1678244001652.jpg" style="width: 150px;">

In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form. (y-3)^4

In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form. (5x – 1)^3

The Binomial Theorem - Example 1

In Exercises 39–48, find the term indicated in each expansion. (x − 1/2)^9; fourth term

In Exercises 1–8, evaluate the given binomial coefficient. <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/be7d5faaccbb1e61-1678244011877.jpg" style="width: 121px;">

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

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

In Exercises 9–30, use the Binomial Theorem to expand each binomial and express the result in simplified form. (x²+2y)^4

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

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)^3

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