Chapter 8: Q. 8.8 (page 909)

Evaluate $\frac{a^{2} - b^{2}}{8 a b^{3}}$ for each value:
$ⓐ a = 1, b = - 1 ⓑ a = \frac{1}{2}, b = - 1 ⓒ a = - 2, b = 1$

Short Answer

Expert verified

$ⓐ The value of \frac{a^{2} - b^{2}}{8 a b^{3}} for a = 1, b = - 1 is 0 . ⓑ The value of \frac{a^{2} - b^{2}}{8 a b^{3}} for a = \frac{1}{2}, b = - 1 is \frac{3}{16} . ⓒ The value of \frac{a^{2} - b^{2}}{8 a b^{3}} for a = - 2, b = 1 is - \frac{3}{16} .$

Step by step solution

Step 1. Given Information

Evaluate $\frac{a^{2} - b^{2}}{8 a b^{3}}$ for each value:

$ⓐ a = 1, b = - 1 ⓑ a = \frac{1}{2}, b = - 1 ⓒ a = - 2, b = 1$

Part (a) Step 1. Finding the value of a2−b28ab3 for a=1, b=−1

Putting $a = 1, b = - 1$ on the given expression

role="math" localid="1648381472744" $\frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{{(1)}^{2} - {(- 1)}^{2}}{8 \cdot 1 \cdot {(- 1)}^{3}} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{1 - 1}{8 \cdot 1 \cdot (- 1)} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{0}{- 8} \frac{a^{2} - b^{2}}{8 a b^{3}} = 0$

Part (b) Step 1. Finding the value of a2−b28ab3 for a=12 , b=−1

Putting $a = \frac{1}{2}, b = - 1$ on the given expression

$\frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{{(\frac{1}{2})}^{2} - {(- 1)}^{2}}{8 \cdot \frac{1}{2} \cdot {(- 1)}^{3}} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{\frac{1}{4} - 1}{4 \cdot (- 1)} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{\frac{1}{4} - 1 \cdot \frac{4}{4}}{- 4} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{\frac{1}{4} - \frac{4}{4}}{- 4} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{\frac{1 - 4}{4}}{- 4} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{- 3}{4} \cdot \frac{1}{- 4} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{3}{16}$

Part (c) Step 1. Finding the value of a2−b28ab3 for a=−2, b=1

Putting $a = - 2, b = 1$ on the given expression

role="math" localid="1648381736852" $\frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{{(- 2)}^{2} - {(1)}^{2}}{8 \cdot (- 2) \cdot {(1)}^{3}} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{4 - 1}{8 \cdot (- 2) \cdot 1} \frac{a^{2} - b^{2}}{8 a b^{3}} = \frac{3}{- 16} \frac{a^{2} - b^{2}}{8 a b^{3}} = - \frac{3}{16}$

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Evaluate $\frac{a^{2} - b^{2}}{8 a b^{3}}$ for each value:
$ⓐ a = 1, b = - 1 ⓑ a = \frac{1}{2}, b = - 1 ⓒ a = - 2, b = 1$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Finding the value of a2−b28ab3 for a=1, b=−1

Part (b) Step 1. Finding the value of a2−b28ab3 for a=12 , b=−1

Part (c) Step 1. Finding the value of a2−b28ab3 for a=−2, b=1

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Evaluate a2−b28ab3for each value:ⓐa=1,b=−1ⓑa=12,b=−1ⓒa=−2,b=1

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Finding the value of a2−b28ab3 for a=1, b=−1

Part (b) Step 1. Finding the value of a2−b28ab3 for a=12 , b=−1

Part (c) Step 1. Finding the value of a2−b28ab3 for a=−2, b=1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Probability and Statistics

Logic and Functions

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Evaluate $\frac{a^{2} - b^{2}}{8 a b^{3}}$ for each value:
$ⓐ a = 1, b = - 1 ⓑ a = \frac{1}{2}, b = - 1 ⓒ a = - 2, b = 1$