Question
upstudy study bank question image url

b) \( a^{3}-b^{3} \) c) \( a^{6}+64 q^{6} \)

Ask by Hart Wang. in Colombia
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

b) \( a^{3}-b^{3} = (a-b)(a^{2}+ab+b^{2}) \) c) \( a^{6}+64 q^{6} = (a^{2}+4q^{2})(a^{4}-4a^{2}q^{2}+16q^{4}) \)

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

Let's dive into the expression \(a^3 - b^3\)! This is a classic difference of cubes and can be factored elegantly using the formula \(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\). Isn’t it lovely how something that looks a bit complicated can be simplified so neatly? This kind of factorization is super handy in algebra and can help you solve equations more efficiently. Now, onto the exciting part about \(a^6 + 64q^6\)! This expression can be recognized as a sum of cubes, as it can be rewritten as \(a^6 + (4q^2)^3\). Which means you can apply the sum of cubes formula: \(x^3 + y^3 = (x + y)(x^2 - xy + y^2)\). So here, let \(x = a^2\) and \(y = 4q^2\). This gives you the delightful factorization \( (a^2 + 4q^2)(a^4 - 4a^2q^2 + 16q^4) \). That’s algebra magic at play!

Latest Algebra Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy