Chapter 6: Q. 404 (page 636)

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$81 m^{3} + 3$

Short Answer

Expert verified

The simplified factor is $3 (3 m + 1) (9 m^{2} - 3 m + 1)$

Step by step solution

Step 1. Given information.

The polynomial expression given is

$81 m^{3} + 3$ .

To find factor using sum and difference of cube following formula are used,

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

Step 2. Calculate the expression.

$81 m^{3} + 3 = 3 (27 m^{3} + 1) = 3 ({(3 m)}^{3} + 1^{3}) = 3 (3 m + 1) (9 m^{2} - 3 m + 1)$

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In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$81 m^{3} + 3$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate the expression.

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In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.81m3+3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$81 m^{3} + 3$