Chapter 7: Q 7.112 (page 864)

Factor: $27 - 8 y^{3}$

Short Answer

Expert verified

The factorization of the expression is $(3 - 2 y) (9 + 6 y + 4 y^{2})$

Step by step solution

Step 1. Given information

Given expression is $27 - 8 y^{3}$

Step 2. Write the terms as a cube a3-b3

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

Step 3. Write the difference in the cubes pattern and simplify.

$(a - b) (a^{2} + a b + b^{2}) = (3 - 2 y) (3^{2} + 3 \times 2 y + {(2 y)}^{2}) = (3 - 2 y) (9 + 6 y + 4 y^{2})$

Step 4. Check

$(3 - 2 y) (9 + 6 y + 4 y^{2}) = 27 - 18 y + 18 y - 12 y^{2} + 12 y^{2} - 8 y^{3} = 27 - 8 y^{3}$

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Factor: $27 - 8 y^{3}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the terms as a cube a3-b3

Step 3. Write the difference in the cubes pattern and simplify.

Step 4. Check

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Factor:27-8y3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the terms as a cube a3-b3

Step 3. Write the difference in the cubes pattern and simplify.

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Study anywhere. Anytime. Across all devices.

Factor: $27 - 8 y^{3}$