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Chapter 8: Q21. (page 514)

Use the Distributive Property to factor each polynomial.

14x2y鈭�21xy+35xy2

Short Answer

Expert verified

The factorization of the given polynomial is 7xy(2x鈭�3+5y).

Step by step solution

01

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

Find the factorization of 14x2y,21xyand 35xy2.

14x2y=2鈰�7鈰�x鈰�x鈰�y21xy=3鈰�7鈰�x鈰�y35xy2=5鈰�7鈰�x鈰�y鈰�y

From the factorization of 14x2y,21xyand 35xy2, it can be noticed that the greatest common factor of 14x2y,21xyand 35xy2is7鈰�x鈰�y or 7xy.

Therefore, the greatest common factor of 14x2y,21xyand 35xy2is 7xy.

02

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

Therefore, it is obtained that:

14x2y鈭�21xy+35xy2=7xy2x鈭�7xy3+7xy5y

03

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

The distributive property states that:

ab+ac=ab+c

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

Therefore, it is obtained that:

14x2y鈭�21xy+35xy2=7xy2x鈭�7xy3+7xy5y=7xy2x鈭�3+5y

Therefore, the factorization of the given polynomial is 7xy2x鈭�3+5y.

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Most popular questions from this chapter

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.

x鈭�2=0炉is a quadratic equation.

Solve each equation. Check your solutions.x2+5x鈭�50=0.

Factor each trinomial, if possible. If the trinomial cannot be factored, write prime.

12x2+22x鈭�14.

Solve each equation. Check your solutions.40x2+2x=24.

Rewrite each expression using the Distributive Property. The simplify,

鈭�6(x2鈭�5x+6)
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