Question

True or False $(x+a)\left(x^{2}+a x+a\right)=x^{3}+a^{3}$

   True or False $(x+a)\left(x^{2}+a x+a\right)=x^{3}+a^{3}$

College Algebra

College Algebra

Michael Sullivan 10th Edition

Chapter 0, Problem 8

Instant Answer

Solved by Expert Adithya Ramanujam

05/07/2020

Step 1

We do this by multiplying $(x+a)$ with each term in $(x^{2}+ax+a)$. Show more…

Show all steps

lock

Thanks for your feedback!

True or False $(x+a)\left(x^{2}+a x+a\right)=x^{3}+a^{3}$

Play audio

Feedback

Powered by NumerAI

Adithya Ramanujam and 62 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Polynomial Multiplication

This concept involves multiplying polynomials by applying the distributive property, where each term of one polynomial is multiplied with every term of the other, and then similar terms are combined. It is a fundamental process in algebra used for expanding and simplifying expressions.

Distributive Property

The distributive property is an algebraic rule that ensures multiplication is distributed over addition. It states that a(b + c) equals ab + ac, and is crucial when expanding expressions by making sure every term is appropriately multiplied.

Algebraic Identities

Algebraic identities are equations that hold true for all variable values and serve as shortcuts for rewriting and simplifying expressions. Recognizing and applying these identities can greatly simplify arithmetic and manipulation of polynomial expressions.

Sum of Cubes Factorization

This specific identity factors a cubic expression of the form x³ + a³ into a product of a binomial and a quadratic: x³ + a³ = (x + a)(x² - ax + a²). Understanding this factorization helps in comparing and verifying polynomial identities by revealing the necessary structure for the equality to hold.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later