Chapter 7: Q. 430 (page 900)

Factor Sums and Differences of Cubes
In the following exercises, factor.
$b^{3} - 216$

Short Answer

Expert verified

The factors for $b^{3} - 216 = (b - 6) (b^{2} + 6 b + 36)$

Step by step solution

Step 1. Given information

The given differences of cubes $b^{3} - 216$

Step 2. Finding the factors for given differences of cubes

We can find the factors as follows

Use the sum product pattern

$b^{3} - 216 = b^{3} - 6^{3} [∵ (a^{3} - b^{3}) = (a - b) (a^{2} + a b + b^{2})] = b^{3} + 6 b^{2} + 36 b - 6 b^{2} - 36 b - 216$

Common factors from the two pairs

$b^{3} + 6 b^{2} + 36 b - 6 b^{2} - 36 b - 216 = b (b^{2} + 6 b + 36) - 6 (b^{2} + 6 b + 36)$

Rewrite in factored form

$b (b^{2} + 6 b + 36) - 6 (b^{2} + 6 b + 36) = (b - 6) (b^{2} + 6 b + 36)$

Therefore,factors for $b^{3} - 216 = (b - 6) (b^{2} + 6 b + 36)$

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Factor Sums and Differences of Cubes
In the following exercises, factor.
$b^{3} - 216$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the factors for given differences of cubes

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Factor Sums and Differences of CubesIn the following exercises, factor.b3-216

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the factors for given differences of cubes

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Decision Maths

Geometry

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Factor Sums and Differences of Cubes
In the following exercises, factor.
$b^{3} - 216$