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Factor
1-p^(3) completely.
Answer:

Factor $1-p^{3}$ completely. $\newline$ Answer:

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Evaluate rational exponents

Full solution

Q. Factor

1-p^{3}

completely.

\newline

Answer:

Identify expression: Identify the expression to be factored. $1 - p^3$ is a difference of cubes since it can be written as $a^3 - b^3$ where $a = 1$ and $b = p$ .
Recall formula: Recall the formula for factoring a difference of cubes. $\newline$ The formula for factoring $a^3 - b^3$ is $(a - b)(a^2 + ab + b^2)$ .
Apply formula: Apply the formula to the given expression. $\newline$ Using the formula, we have $a = 1$ and $b = p$ , so the factorization of $1 - p^3$ is $(1 - p)(1^2 + 1\cdot p + p^2)$ .
Simplify factors: Simplify the factors. $\newline$ $(1 - p)(1 + p + p^2)$ simplifies to $(1 - p)(1 + p + p^2)$ since $1^2 = 1$ .

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