Chapter 6: Q. 398 (page 635)

In the following exercises, factor completely using the difference of squares pattern, if possible.
$48 m^{4} n^{2} - 243 n^{2}$

Short Answer

Expert verified

The Factored form of given polynomial is,

$3 n^{2} (4 m - 9 n) (4 m + 9 n)$

Step by step solution

Step 1. Given Information

We are given a polynomial,

$48 m^{4} n^{2} - 243 n^{2}$

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

Factoring out greatest common factor $3 n^{2}$ , we get

localid="1644736388246" $\begin{array}{l} 48 m^{4} n^{2} - 243 n^{2} = 3 n^{2} (16 m^{2} - 81 n^{2}) \\ 48 m^{4} n^{2} - 243 n^{2} = 3 n^{2} ((4 m)^{2} - (9 n)^{2}) \end{array}$

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

$48 m^{4} n^{2} - 243 n^{2} = 3 n^{2} (4 m - 9 n) (4 m + 9 n)$

Step 3. Checking the factorization by multiplying

$3 n^{2} (4 m - 9 n) (4 m + 9 n) = 48 m^{4} n^{2} - 243 n^{2} 3 n^{2} (16 m^{2} + 36 m n - 36 m x - 81 n^{2}) = 48 m^{4} n^{2} - 243 n^{2} 3 n^{2} (16 m^{2} - 81 n^{2}) = 48 m^{4} n^{2} - 243 n^{2} 48 m^{4} n^{2} - 243 n^{2} = 48 m^{4} n^{2} - 243 n^{2} L H S = R H S$

Hence the factorization is correct.

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In the following exercises, factor completely using the difference of squares pattern, if possible.
$48 m^{4} n^{2} - 243 n^{2}$

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.48m4n2−243n2

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

Probability and Statistics

Applied Mathematics

Calculus

Geometry

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely using the difference of squares pattern, if possible.
$48 m^{4} n^{2} - 243 n^{2}$