Podcast
Questions and Answers
What is the expanded form of $(a + b)³$?
What is the expanded form of $(a + b)³$?
Which term in the expansion of $(a + b)³$ represents the product of $a$ and $b$?
Which term in the expansion of $(a + b)³$ represents the product of $a$ and $b$?
What is the coefficient of the $a^2b$ term in the expansion of $(a + b)³$?
What is the coefficient of the $a^2b$ term in the expansion of $(a + b)³$?
If $a = 1$ and $b = 1$, what is the value of $(a + b)³$?
If $a = 1$ and $b = 1$, what is the value of $(a + b)³$?
Signup and view all the answers
Which of the following is a valid application of $(a + b)³$?
Which of the following is a valid application of $(a + b)³$?
Signup and view all the answers
Study Notes
Expansion of $(a + b)³$
- The expanded form of $(a + b)³$ is given by the formula: [(a + b)³ = a³ + 3a²b + 3ab² + b³]
- This expansion involves combining terms with varying powers of (a) and (b).
Term Representing the Product of $a$ and $b$
- The term in the expansion that represents the product of (a) and (b) is (3a²b).
- This term indicates that (a) is squared while (b) appears linearly, embodying their mixed product.
Coefficient of the $a²b$ Term
- The coefficient of the (a²b) term in the expansion is (3).
- This reflects how many ways we can select one (b) from the three total factors of ((a + b)) when expanding.
Value of $(a + b)³$ When (a = 1) and (b = 1)
- If (a = 1) and (b = 1), then: [(1 + 1)³ = 2³ = 8]
- This demonstrates the calculation of the cubic expansion at specific input values.
Valid Application of $(a + b)³$
- The expression $(a + b)³$ can be applied in various algebraic contexts, including polynomial expansions, binomial theorem applications, and combinatorial problems.
- It proves useful in solving real-world problems involving volume calculations when combining different quantities.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on the expansion of the binomial expression (a + b)³. Answer questions about the coefficients, terms, and specific values when a and b are given. Explore key applications of the binomial theorem as you delve into this algebra quiz.
