Question

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Explanation:

1. The process of decomposing expressions into simpler factors is formally called factoring.
2. The difference of two cubes formula is often used to calculate volume differences of 3D objects (e.g., cubes of different side lengths).
3. The difference of two cubes factoring rule only applies when both terms are perfect cubes (terms that are the cube of an integer or variable expression).
4. Factoring differences of cubes builds foundational algebraic skills needed for higher-level math like algebra II, calculus, or abstract algebra.
5. The formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ rewrites the original expression as the product of two simpler expressions.

Answer:

1. factoring
2. volumes (or 3D measurements)
3. perfect cubes
4. algebra (or calculus/advanced math topics)
5. product