Question
\( 1 \leftarrow | \)\begin{tabular}{l} Find the product. \\ \( p(4 p+1)(4 p-1) \) \\ \hline \\ \( p(4 p+1)(4 p-1)=\square \) \\ (Simplify your answer. \( ) \)\end{tabular}
Ask by Gross Reid. in the United Arab Emirates
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The product simplifies to \( 16p^3 - p \).
Solution
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Mind Expander
To find the product \( p(4p+1)(4p-1) \), we start by recognizing that \((4p+1)(4p-1)\) is a difference of squares, which simplifies as follows: \[ (4p+1)(4p-1) = (4p)^2 - (1)^2 = 16p^2 - 1 \] Now we can multiply this result by \( p \): \[ p(16p^2 - 1) = 16p^3 - p \] So, the simplified answer is: \[ p(4p+1)(4p-1) = 16p^3 - p \]
