Chapter 7: Q. 300 (page 878)

In the following exercises, factor completely.
$m^{4} - 81$

Short Answer

Expert verified

The factored form of the polynomial is $(m^{2} + 9) (m^{2} - 9) .$

Step by step solution

Step 1. Given Information.

The given polynomial is $m^{4} - 81 .$

Step 2. Factoring by the difference of squares

There is no GCF in the given polynomial.

The polynomial is a binomial and it is the type of difference of squares.

To factor, the given polynomial completely writes it as a product of conjugates.

So,

$m^{4} - 81 = {(m^{2})}^{2} - {(9)}^{2} = (m^{2} - 9) (m^{2} + 9)$

The polynomial is factored completely.

Thus, the factored form is $(m^{2} - 9) (m^{2} + 9) .$

Step 3. Check the answer

To check the answer, expand the factored form we get,

$m^{4} - 81 = (m^{2} + 9) (m^{2} - 9) m^{4} - 81 = m^{4} + 9 m^{2} - 9 m^{2} - 81 m^{4} - 81 = m^{4} - 81$

L.H.S = R.H.S

Thus, the answer is right.

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In the following exercises, factor completely.
$m^{4} - 81$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factoring by the difference of squares

Step 3. Check the answer

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In the following exercises, factor completely.m4-81

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factoring by the difference of squares

Step 3. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Statistics

Calculus

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely.
$m^{4} - 81$