Chapter 6: Q. 456 (page 638)

In the following exercises, factor completely.
$32 x^{5} y^{2} - 162 x y^{2}$

Short Answer

Expert verified

On factoring, we get $2 x y^{2} (4 x^{2} + 9) (2 x + 3) (2 x - 3)$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$32 x^{5} y^{2} - 162 x y^{2}$

Factor out the GCF,

$= 2 x y^{2} (16 x^{4} - 81)$

Write using the difference of square pattern,

$= 2 x y^{2} {{(4 x^{2})}^{2} - 9^{2}} = 2 x y^{2} (4 x^{2} + 9) (4 x^{2} - 9)$

Write using the sum of square pattern,

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

Step 2. Check the answers.

Check by multiplying,

$= 2 x y^{2} (4 x^{2} + 9) (2 x + 3) (2 x - 3) = 2 x y^{2} (4 x^{2} + 9) (4 x^{2} - 6 x + 6 x - 9) = 2 x y^{2} (4 x^{2} + 9) (4 x^{2} - 9) = 2 x y^{2} (16 x^{4} - 36 x^{2} + 36 x^{2} - 81) = 2 x y^{2} (16 x^{4} - 81) = 32 x^{5} y^{2} - 162 x y^{2}$

This is true.

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In the following exercises, factor completely.
$32 x^{5} y^{2} - 162 x y^{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check the answers.

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In the following exercises, factor completely.32x5y2-162xy2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check the answers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Statistics

Calculus

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely.
$32 x^{5} y^{2} - 162 x y^{2}$