Question

Factor each expression. $$ 1-(x+y)^{3} $$

   Factor each expression.
$$
1-(x+y)^{3}
$$

Intermediate Algebra

Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 5, Problem 94

Instant Answer

Solved by Expert Amy Jiang

08/01/2020

Step 1

The formula for the difference of cubes is $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$. Show more…

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Factor each expression. $$ 1-(x+y)^{3} $$

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Key Concepts

Rewriting Constants as Cubes

In many algebraic expressions, constants can be rewritten as power terms to match a specific pattern; for example, 1 can be expressed as 1^3. This insight allows you to apply the difference of cubes formula, highlighting the intersection between simple numerical identities and advanced factoring techniques.

Difference of Cubes Factorization

This concept involves recognizing when an expression fits the form a^3 - b^3, which factors into (a - b)(a^2 + ab + b^2). The key is to identify the cube structure in both terms, enabling a systematic factorization of the polynomial.

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