Chapter 6: Q. 413 (page 636)

Recognize and Use the Appropriate Method to Factor a Polynomial Completely.
$b^{3} - 64$

Short Answer

Expert verified

The factors of the given expression are $(b - 4) (b^{2} + 4 b + 16)$ .

Step by step solution

Step 1. Given and explanation

We have $b^{3} - 64$ .

We can see that this forms a pattern of difference of two perfect cubes.

We know that ${(a)}^{3} - {(b)}^{3} = (a - b) (a^{2} + a b + b^{2})$ .

Applying this, we will factorize the given expression.

Step 2. Factorizing the expression.

We have $b^{3} - 64$ .

This can be written as ${(b)}^{3} - {(4)}^{3}$ .

Applying the property ${(a)}^{3} - {(b)}^{3} = (a - b) (a^{2} + a b + b^{2})$ , we get

${(b)}^{3} - {(4)}^{3} = (b - 4) (b^{2} + 4 b + 16)$

This cannot be further factorized, so the factors of the given expression are $(b - 4) (b^{2} + 4 b + 16)$ .

Step 3. Check the solution.

We will check the solution by simply multiplying the resulting factors.

If we get the given equation as a product, our factorization is right.

So,

$= (b - 4) (b^{2} + 4 b + 16) = b^{3} + 4 b^{2} + 16 b - 4 b^{2} - 16 b - 64 = b^{3} - 64$

Thus our calculations are right.

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Recognize and Use the Appropriate Method to Factor a Polynomial Completely.
$b^{3} - 64$

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Factorizing the expression.

Step 3. Check the solution.

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Recognize and Use the Appropriate Method to Factor a Polynomial Completely.b3-64

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Factorizing the expression.

Step 3. Check the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Statistics

Mechanics Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Recognize and Use the Appropriate Method to Factor a Polynomial Completely.
$b^{3} - 64$