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Chapter 6: Q. 196 (page 603)

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
n6+512

Short Answer

Expert verified

The factored form of the given expression is (n2+8)(n4-8n2+64).

Step by step solution

01

Step 1. Given information.

The given expression is:
n6+512

02

Step 2. Determine the factored form.

The given expression can be written as:
n6+512=(n2)3+83=(n2+8)(n2)2-(n2)(8)+82鈭�a3+b3=(a+b)(a2-ab+b2)=(n2+8)n4-8n2+64

03

Step 3. Conclusion.

The factored form of the given expression is (n2+8)(n4-8n2+64).

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