Chapter 6: Q. 388 (page 635)

In the following exercises, factor completely using the difference of squares pattern, if possible.
$81 r^{2} - 25$

Short Answer

Expert verified

The Factored form of given polynomial is $(9 r - 5) (9 r + 5)$ .

Step by step solution

Step 1. Given Information

We are given a polynomial,

$81 r^{2} - 25$

The formula used for factoring using the difference of squares pattern is

$a^{2} - b^{2} = (a + b) (a - b)$ .

Step 2. Factorizing the polynomial

The given polynomial can be written as,

$81 r^{2} - 25 = (9 r) - 5^{2}$

Using $a^{2} - b^{2} = (a + b) (a - b)$ , we get

$81 r^{2} - 25 = (9 r - 5) (9 r + 5)$

Step 3. Checking the factorization by multiplying

Multiplying the factors, we get

$(9 r - 5) (9 r + 5) = 81 r^{2} - 25 {(9 r)}^{2} + 5 \times 9 r - 5 \times 9 r - 5^{2} = 81 r^{2} - 25 81 r^{2} - 25 = 81 r^{2} - 25 L H S = R H S$

Hence the factorization is correct.

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In the following exercises, factor completely using the difference of squares pattern, if possible.
$81 r^{2} - 25$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factorizing the polynomial

Step 3. Checking the factorization by multiplying

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In the following exercises, factor completely using the difference of squares pattern, if possible.81r2−25

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factorizing the polynomial

Step 3. Checking the factorization by multiplying

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely using the difference of squares pattern, if possible.
$81 r^{2} - 25$