Chapter 7: Q 7.113 (page 865)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

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

Step 2. Write the terms as a cube.

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

Step 3. Use the difference of cube pattern and simplify.

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

Step 4. Check

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

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the terms as a cube.

Step 3. Use the difference of cube pattern and simplify.

Step 4. Check

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Factor:8x3-27y3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the terms as a cube.

Step 3. Use the difference of cube 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

Calculus

Applied Mathematics

Geometry

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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