Chapter 8: Q21. (page 514)

Use the Distributive Property to factor each polynomial.
$14 x^{2} y - 21 x y + 35 x y^{2}$

Short Answer

Expert verified

The factorization of the given polynomial is $7 x y (2 x - 3 + 5 y)$ .

Step by step solution

Step 1. Find the greatest common factor of 14x2y,21xy and 35xy2.

Find the factorization of $14 x^{2} y, 21 x y$ and $35 x y^{2}$ .

$14 x^{2} y = 2 \cdot 7 \cdot x \cdot x \cdot y 21 x y = 3 \cdot 7 \cdot x \cdot y 35 x y^{2} = 5 \cdot 7 \cdot x \cdot y \cdot y$

From the factorization of $14 x^{2} y, 21 x y$ and $35 x y^{2}$ , it can be noticed that the greatest common factor of $14 x^{2} y, 21 x y$ and $35 x y^{2}$ is $7 \cdot x \cdot y$ or $7 x y$ .

Therefore, the greatest common factor of $14 x^{2} y, 21 x y$ and $35 x y^{2}$ is $7 x y$ .

Step 2. Write each term as the product of the greatest common factor and the remaining factors.

Therefore, it is obtained that:

$14 x^{2} y - 21 x y + 35 x y^{2} = 7 x y (2 x) - 7 x y (3) + 7 x y (5 y)$

Step 3. Use the distributive property to factor out the greatest common factor.

The distributive property states that:

$a b + a c = a (b + c)$

Now, use the distributive property to factor out the greatest common factor.

Therefore, it is obtained that:

$14 x^{2} y - 21 x y + 35 x y^{2} = 7 x y (2 x) - 7 x y (3) + 7 x y (5 y) = 7 x y (2 x - 3 + 5 y)$

Therefore, the factorization of the given polynomial is $7 x y (2 x - 3 + 5 y)$ .

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Use the Distributive Property to factor each polynomial.
$14 x^{2} y - 21 x y + 35 x y^{2}$

Short Answer

Step by step solution

Step 1. Find the greatest common factor of 14x2y,21xy and 35xy2.

Step 2. Write each term as the product of the greatest common factor and the remaining factors.

Step 3. Use the distributive property to factor out the greatest common factor.

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Use the Distributive Property to factor each polynomial.14x2y−21xy+35xy2

Short Answer

Step by step solution

Step 1. Find the greatest common factor of 14x2y,21xy and 35xy2.

Step 2. Write each term as the product of the greatest common factor and the remaining factors.

Step 3. Use the distributive property to factor out the greatest common factor.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Statistics

Calculus

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Use the Distributive Property to factor each polynomial.
$14 x^{2} y - 21 x y + 35 x y^{2}$