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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 6: Q. 773 (page 806)

In the following exercises, simplify each expression.
$\frac{64 x^{3} - 1}{4 x - 1}$ .

Short Answer

Expert verified

The simplified expression for $\frac{64 x^{3} - 1}{4 x - 1}$ is, $(4 x - 1) (16 x^{2} + 4 x + 1)$ .

Step by step solution

01

Step 1. Given information

$\frac{64 x^{3} - 1}{4 x - 1}$ .

We need to simplify the given expression.

02

Step 2.Let us perform the division to get the simplified expression.

$4 x - 1 \begin{matrix} 16 x^{2} + & 4 x + & 1 \end{matrix} \begin{matrix} 64 x^{3} - & 1 \end{matrix} \begin{matrix} 64 x^{3} - & 16 x^{2} \end{matrix} \begin{matrix} 16 x^{2} - & 1 \end{matrix} \begin{matrix} 16 x^{2} - & 4 x \end{matrix} \begin{matrix} 0 & 4 x - & 1 \end{matrix} \begin{matrix} 4 x & - 1 \end{matrix} 0$

From the division, the simplified expression is, $(4 x - 1) (16 x^{2} + 4 x + 1)$ .

To check, multiply $(4 x - 1) (16 x^{2} + 4 x + 1)$ .

The result should be $64 x^{3} - 1$ .

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