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Chapter 7: Q 238. (page 867)

In the following exercises, factor.
49x2-81y2

Short Answer

Expert verified

The factorization of49x2-81y2is,(7x-9y)(7x+9y)

Step by step solution

01

Step 1. Given information 

Given expression is49x2-81y2.

02

Step 2. Does the binomial fit the pattern?

Is this a difference?

Yes, it is a difference.

49x2-81y2

Are the first and last terms perfect squares?

yes, the first and last terms perfect squares.

49x2-81y2

03

Step 3. Write them as squares.

(a)2-(b)2=(7x)2-(9y)2

04

Step 4. Write the product of conjugates.

(a-b)(a+b)=(7x-9y)(7x+9y)

05

Step 5. Check by multiplying.

(7x-9y)(7x+9y)=49x2-81y2

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