Chapter 7: Q 7.21. (page 815)

Factor: $9 x y^{2} + 6 x^{2} y^{2} + 21 y^{3}$

Short Answer

Expert verified

The required factor is $3 y^{2} (3 x + 2 x^{2} + 7 y)$ .

Step by step solution

Step 1. Given information.

The given polynomial is:

$9 x y^{2} + 6 x^{2} y^{2} + 21 y^{3}$

Step 2. Find the GCF.

Find the GCF of $9 x y^{2}, 6 x^{2} y^{2}, and 21 y^{3}$ ,

role="math" localid="1647710482910" $9 x y^{2} = 3 \cdot 3 \cdot x \cdot y \cdot y 6 x^{2} y^{2} = 2 \cdot 3 \cdot x \cdot x \cdot y \cdot y 21 y^{3} = 3 \cdot 7 \cdot y \cdot y \cdot y$

GCF is:

role="math" localid="1647710505787" $= 3 \cdot y \cdot y = 3 y^{2}$

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$3 y^{2} \cdot 3 x + 3 y \cdot 2 x^{2} + 3 y \cdot 7 y$

Factor the GCF,

$3 y^{2} (3 x + 2 x^{2} + 7 y)$

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Factor: $9 x y^{2} + 6 x^{2} y^{2} + 21 y^{3}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the GCF.

Step 3. Find the factor.

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Factor:9xy2+6x2y2+21y3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the GCF.

Step 3. Find the factor.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Statistics

Study anywhere. Anytime. Across all devices.

Factor: $9 x y^{2} + 6 x^{2} y^{2} + 21 y^{3}$