1. Fundamental Concepts of Algebra

2. Equations and Inequalities

3. Functions and Graphs

4. Polynomial and Rational Functions

5. Exponential and Logarithmic Functions

6. Systems of Equations and Inequalities

7. Matrices and Determinants

8. Conic Sections

9. Sequences, Induction, and Probability

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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

Exercises 89–91 will help you prepare for the material covered in the next section. Evaluate n!/(n-r)! for n = 20 and r = 3

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

Exercises 89–91 will help you prepare for the material covered in the next section. Evaluate n!/(n-r)!r! for n = 8 and r = 3

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;">

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. (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

Expand a Binomial Raised to a Power

The Binomial Theorem

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

Find the term in the expansion of (x² + y²)^5 containing x^4 as a factor.

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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College Algebra

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Find the Common Difference for an Arithmetic Sequence

Write Terms of an Arithmetic Sequence

Use the Formula for the General Term of an Arithmetic Sequence

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence

Arithmetic Sequences

Compute Empirical Probability

Compute Theoretical Probability

Find the Probability that an Event will Not Occur

Find the Probability of One Event or a Second Event Occurring

Find the Probability of One Event and a Second Event Occurring

Probability

Evaluate a Binomial Coefficient

Use the Fundamental Counting Principle

Distinguish Between Permutation and Combination Problems

Use the Permutations Formula

Counting Principles, Permutations, and Combinations

Find Particular Terms of a Sequence from the General Term

Use Recursion Formulas

Use Factorial Notation

Use Summation Notation

Sequences and Summation Notation

Understand the Principle of Mathematical Induction

Prove Statements Using Mathematical Induction

Mathematical Induction

Find the Common Ratio of a Geometric Sequence