Understanding Sum and Difference of Cubes
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Beginner
Start here! Easy to understand
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Beginner Explanation
A sum of cubes x^3 + y^3 factors as (x+y)(x^2 - xy + y^2). For example, 8x^3 + 27 = (2x + 3)(4x^2 - 6x + 9).
Practice Problems
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1
Quick Quiz
Single Choice Quiz
Beginner
What is the factored form of $8x^3 + 27$?
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2
Real-World Problem
Question Exercise
Intermediate
Teenager Scenario
You have a cubic block of side a and a smaller cube of side b. Express the volume difference between the two cubes using the difference of cubes formula a^3 - b^3 = (a-b)(a^2 + ab + b^2).
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3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
Determine the factors of $64y^3 - 1$ using the difference of cubes.
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4
Challenge Quiz
Single Choice Quiz
Advanced
What is the factored form of $27p^3 + q^3$?
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